[{"citation":{"chicago":"Kirschmer, Markus, and Michael H. Mertens. “On an Analogue to the Lucas-Lehmer-Riesel Test Using Elliptic Curves.” In <i>Integers</i>. DE GRUYTER, 2013. <a href=\"https://doi.org/10.1515/9783110298161.212\">https://doi.org/10.1515/9783110298161.212</a>.","short":"M. Kirschmer, M.H. Mertens, in: Integers, DE GRUYTER, 2013.","apa":"Kirschmer, M., &#38; Mertens, M. H. (2013). On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves. In <i>Integers</i>. DE GRUYTER. <a href=\"https://doi.org/10.1515/9783110298161.212\">https://doi.org/10.1515/9783110298161.212</a>","ieee":"M. Kirschmer and M. H. Mertens, “On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves,” in <i>Integers</i>, DE GRUYTER, 2013.","ama":"Kirschmer M, Mertens MH. On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves. In: <i>Integers</i>. DE GRUYTER; 2013. doi:<a href=\"https://doi.org/10.1515/9783110298161.212\">10.1515/9783110298161.212</a>","bibtex":"@inbook{Kirschmer_Mertens_2013, title={On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves}, DOI={<a href=\"https://doi.org/10.1515/9783110298161.212\">10.1515/9783110298161.212</a>}, booktitle={Integers}, publisher={DE GRUYTER}, author={Kirschmer, Markus and Mertens, Michael H.}, year={2013} }","mla":"Kirschmer, Markus, and Michael H. Mertens. “On an Analogue to the Lucas-Lehmer-Riesel Test Using Elliptic Curves.” <i>Integers</i>, DE GRUYTER, 2013, doi:<a href=\"https://doi.org/10.1515/9783110298161.212\">10.1515/9783110298161.212</a>."},"publication":"Integers","extern":"1","abstract":[{"lang":"eng","text":"Following an idea of B. H. Gross, who presented an elliptic curve test for Mersenneprimes Mₚ=2ᵖ−1, we propose a similar test with elliptic curves for generalizedThabit primesK(h, n) := h·2ⁿ−1 for any positive odd number h and any integer n> log₂(h)+2."}],"date_created":"2023-03-07T08:51:46Z","department":[{"_id":"102"}],"type":"book_chapter","author":[{"id":"82258","last_name":"Kirschmer","first_name":"Markus","full_name":"Kirschmer, Markus"},{"full_name":"Mertens, Michael H.","last_name":"Mertens","first_name":"Michael H."}],"publication_identifier":{"isbn":["9783110298116"]},"title":"On an analogue to the Lucas-Lehmer-Riesel test using elliptic curves","status":"public","year":"2013","publication_status":"published","date_updated":"2023-04-04T09:17:32Z","language":[{"iso":"eng"}],"_id":"42805","publisher":"DE GRUYTER","user_id":"93826","doi":"10.1515/9783110298161.212"},{"language":[{"iso":"eng"}],"doi":"10.1112/s1461157013000107","publication_identifier":{"issn":["1461-1570"]},"author":[{"full_name":"Lorch, David","last_name":"Lorch","first_name":"David"},{"last_name":"Kirschmer","first_name":"Markus","full_name":"Kirschmer, Markus","id":"82258"}],"title":"Single-class genera of positive integral lattices","year":"2013","intvolume":"        16","publication_status":"published","date_updated":"2023-04-04T07:57:04Z","date_created":"2023-03-07T08:34:28Z","department":[{"_id":"102"}],"keyword":["Computational Theory and Mathematics","General Mathematics"],"type":"journal_article","publication":"LMS Journal of Computation and Mathematics","extern":"1","abstract":[{"text":"We give an enumeration of all positive definite primitive Z-lattices in dimension n ≥ 3 whose genus consists of a single isometry class. This is achieved by using bounds obtained from the Smith–Minkowski–Siegel mass formula to computationally construct the square-free determinant lattices with this property, and then repeatedly calculating pre-images under a mapping first introduced by G. L. Watson.\r\n\r\nWe hereby complete the classification of single-class genera in dimensions 4 and 5 and correct some mistakes in Watson’s classifications in other dimensions. A list of all single-class primitive Z-lattices has been compiled and incorporated into the Catalogue of Lattices.","lang":"eng"}],"publisher":"Wiley","_id":"42796","page":"172-186","volume":16,"user_id":"93826","status":"public","citation":{"mla":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” <i>LMS Journal of Computation and Mathematics</i>, vol. 16, Wiley, 2013, pp. 172–86, doi:<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>.","ama":"Lorch D, Kirschmer M. Single-class genera of positive integral lattices. <i>LMS Journal of Computation and Mathematics</i>. 2013;16:172-186. doi:<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>","bibtex":"@article{Lorch_Kirschmer_2013, title={Single-class genera of positive integral lattices}, volume={16}, DOI={<a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Lorch, David and Kirschmer, Markus}, year={2013}, pages={172–186} }","apa":"Lorch, D., &#38; Kirschmer, M. (2013). Single-class genera of positive integral lattices. <i>LMS Journal of Computation and Mathematics</i>, <i>16</i>, 172–186. <a href=\"https://doi.org/10.1112/s1461157013000107\">https://doi.org/10.1112/s1461157013000107</a>","ieee":"D. Lorch and M. Kirschmer, “Single-class genera of positive integral lattices,” <i>LMS Journal of Computation and Mathematics</i>, vol. 16, pp. 172–186, 2013, doi: <a href=\"https://doi.org/10.1112/s1461157013000107\">10.1112/s1461157013000107</a>.","short":"D. Lorch, M. Kirschmer, LMS Journal of Computation and Mathematics 16 (2013) 172–186.","chicago":"Lorch, David, and Markus Kirschmer. “Single-Class Genera of Positive Integral Lattices.” <i>LMS Journal of Computation and Mathematics</i> 16 (2013): 172–86. <a href=\"https://doi.org/10.1112/s1461157013000107\">https://doi.org/10.1112/s1461157013000107</a>."}},{"doi":"10.1142/s1793042112500492","language":[{"iso":"eng"}],"intvolume":"         8","date_updated":"2023-03-02T14:10:38Z","publication_status":"published","author":[{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"}],"publication_identifier":{"issn":["1793-0421","1793-7310"]},"year":"2012","title":"The Distribution of Number Fields with Wreath Products as Galois Groups ","department":[{"_id":"102"}],"type":"journal_article","date_created":"2022-12-22T10:55:47Z","abstract":[{"text":"Let G be a wreath product of the form C₂ ≀ H, where C₂ is the cyclic group of order 2. Under mild conditions for H we determine the asymptotic behavior of the counting functions for number fields K/k with Galois group G and bounded discriminant. Those counting functions grow linearly with the norm of the discriminant and this result coincides with a conjecture of Malle. Up to a constant factor these groups have the same asymptotic behavior as the conjectured one for symmetric groups. ","lang":"eng"}],"publication":"International Journal of Number Theory","issue":"03","volume":"08","user_id":"21202","_id":"34847","publisher":"World Scientific Pub Co Pte Lt","page":"845-858","status":"public","external_id":{"arxiv":["1108.5597 "]},"citation":{"ama":"Klüners J. The Distribution of Number Fields with Wreath Products as Galois Groups . <i>International Journal of Number Theory</i>. 2012;08(03):845-858. doi:<a href=\"https://doi.org/10.1142/s1793042112500492\">10.1142/s1793042112500492</a>","bibtex":"@article{Klüners_2012, title={The Distribution of Number Fields with Wreath Products as Galois Groups }, volume={08}, DOI={<a href=\"https://doi.org/10.1142/s1793042112500492\">10.1142/s1793042112500492</a>}, number={03}, journal={International Journal of Number Theory}, publisher={World Scientific Pub Co Pte Lt}, author={Klüners, Jürgen}, year={2012}, pages={845–858} }","mla":"Klüners, Jürgen. “The Distribution of Number Fields with Wreath Products as Galois Groups .” <i>International Journal of Number Theory</i>, vol. 08, no. 03, World Scientific Pub Co Pte Lt, 2012, pp. 845–58, doi:<a href=\"https://doi.org/10.1142/s1793042112500492\">10.1142/s1793042112500492</a>.","chicago":"Klüners, Jürgen. “The Distribution of Number Fields with Wreath Products as Galois Groups .” <i>International Journal of Number Theory</i> 08, no. 03 (2012): 845–58. <a href=\"https://doi.org/10.1142/s1793042112500492\">https://doi.org/10.1142/s1793042112500492</a>.","short":"J. Klüners, International Journal of Number Theory 08 (2012) 845–858.","apa":"Klüners, J. (2012). The Distribution of Number Fields with Wreath Products as Galois Groups . <i>International Journal of Number Theory</i>, <i>08</i>(03), 845–858. <a href=\"https://doi.org/10.1142/s1793042112500492\">https://doi.org/10.1142/s1793042112500492</a>","ieee":"J. Klüners, “The Distribution of Number Fields with Wreath Products as Galois Groups ,” <i>International Journal of Number Theory</i>, vol. 08, no. 03, pp. 845–858, 2012, doi: <a href=\"https://doi.org/10.1142/s1793042112500492\">10.1142/s1793042112500492</a>."}},{"doi":"10.1090/s0025-5718-2011-02570-6","language":[{"iso":"eng"}],"date_updated":"2023-04-04T09:22:22Z","publication_status":"published","intvolume":"        81","year":"2012","title":"A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$","author":[{"id":"82258","last_name":"Kirschmer","first_name":"Markus","full_name":"Kirschmer, Markus"}],"publication_identifier":{"issn":["0025-5718","1088-6842"]},"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","Algebra and Number Theory"],"department":[{"_id":"102"}],"date_created":"2023-03-07T08:35:56Z","abstract":[{"lang":"eng","text":"An efficient algorithm to compute automorphism groups and isometries of definite Fq[t]-lattices for odd q is presented. The algorithm requires several square root computations in Fq₂ but no enumeration of orbits having more than eight elements. "}],"extern":"1","publication":"Mathematics of Computation","issue":"279","user_id":"93826","volume":81,"page":"1619-1634","_id":"42797","publisher":"American Mathematical Society (AMS)","status":"public","citation":{"chicago":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” <i>Mathematics of Computation</i> 81, no. 279 (2012): 1619–34. <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">https://doi.org/10.1090/s0025-5718-2011-02570-6</a>.","short":"M. Kirschmer, Mathematics of Computation 81 (2012) 1619–1634.","ieee":"M. Kirschmer, “A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$,” <i>Mathematics of Computation</i>, vol. 81, no. 279, pp. 1619–1634, 2012, doi: <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>.","apa":"Kirschmer, M. (2012). A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. <i>Mathematics of Computation</i>, <i>81</i>(279), 1619–1634. <a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">https://doi.org/10.1090/s0025-5718-2011-02570-6</a>","bibtex":"@article{Kirschmer_2012, title={A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$}, volume={81}, DOI={<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>}, number={279}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Kirschmer, Markus}, year={2012}, pages={1619–1634} }","ama":"Kirschmer M. A normal form for definite quadratic forms over $\\mathbb{F}_{q}[t]$. <i>Mathematics of Computation</i>. 2012;81(279):1619-1634. doi:<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>","mla":"Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\\mathbb{F}_{q}[t]$.” <i>Mathematics of Computation</i>, vol. 81, no. 279, American Mathematical Society (AMS), 2012, pp. 1619–34, doi:<a href=\"https://doi.org/10.1090/s0025-5718-2011-02570-6\">10.1090/s0025-5718-2011-02570-6</a>."}},{"intvolume":"      2011","date_updated":"2023-03-06T09:07:46Z","publication_status":"published","author":[{"full_name":"Fouvry, Étienne","last_name":"Fouvry","first_name":"Étienne"},{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"}],"publication_identifier":{"issn":["1687-0247","1073-7928"]},"year":"2011","title":"Weighted Distribution of the 4-rank of Class Groups and Applications","doi":"10.1093/imrn/rnq223","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We prove that the distribution of the values of the 4-rank of ideal class groups of quadratic fields is not affected when it is weighted by a divisor type function. We then give several applications concerning a new lower bound of the sums of class numbers of real quadratic fields with discriminant less than a bound tending to infinity and several questions of P. Sarnak concerning reciprocal geodesics."}],"issue":"16","publication":"International Mathematics Research Notices","department":[{"_id":"102"}],"keyword":["General Mathematics"],"type":"journal_article","date_created":"2022-12-23T09:08:00Z","status":"public","volume":2011,"user_id":"93826","_id":"34885","publisher":"Oxford University Press (OUP)","page":"3618-3656","citation":{"ieee":"É. Fouvry and J. Klüners, “Weighted Distribution of the 4-rank of Class Groups and Applications,” <i>International Mathematics Research Notices</i>, vol. 2011, no. 16, pp. 3618–3656, 2011, doi: <a href=\"https://doi.org/10.1093/imrn/rnq223\">10.1093/imrn/rnq223</a>.","apa":"Fouvry, É., &#38; Klüners, J. (2011). Weighted Distribution of the 4-rank of Class Groups and Applications. <i>International Mathematics Research Notices</i>, <i>2011</i>(16), 3618–3656. <a href=\"https://doi.org/10.1093/imrn/rnq223\">https://doi.org/10.1093/imrn/rnq223</a>","chicago":"Fouvry, Étienne, and Jürgen Klüners. “Weighted Distribution of the 4-Rank of Class Groups and Applications.” <i>International Mathematics Research Notices</i> 2011, no. 16 (2011): 3618–56. <a href=\"https://doi.org/10.1093/imrn/rnq223\">https://doi.org/10.1093/imrn/rnq223</a>.","short":"É. Fouvry, J. Klüners, International Mathematics Research Notices 2011 (2011) 3618–3656.","mla":"Fouvry, Étienne, and Jürgen Klüners. “Weighted Distribution of the 4-Rank of Class Groups and Applications.” <i>International Mathematics Research Notices</i>, vol. 2011, no. 16, Oxford University Press (OUP), 2011, pp. 3618–56, doi:<a href=\"https://doi.org/10.1093/imrn/rnq223\">10.1093/imrn/rnq223</a>.","bibtex":"@article{Fouvry_Klüners_2011, title={Weighted Distribution of the 4-rank of Class Groups and Applications}, volume={2011}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnq223\">10.1093/imrn/rnq223</a>}, number={16}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2011}, pages={3618–3656} }","ama":"Fouvry É, Klüners J. Weighted Distribution of the 4-rank of Class Groups and Applications. <i>International Mathematics Research Notices</i>. 2011;2011(16):3618-3656. doi:<a href=\"https://doi.org/10.1093/imrn/rnq223\">10.1093/imrn/rnq223</a>"}},{"language":[{"iso":"eng"}],"doi":"10.1016/j.jsc.2012.05.010","author":[{"full_name":"van Hoeij, Mark","last_name":"van Hoeij","first_name":"Mark"},{"id":"21202","last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"},{"first_name":"Andrew","last_name":"Novocin","full_name":"Novocin, Andrew"}],"publication_identifier":{"issn":["0747-7171"]},"title":"Generating subfields","year":"2011","intvolume":"        52","publication_status":"published","date_updated":"2023-03-06T09:46:15Z","date_created":"2022-12-22T10:54:15Z","department":[{"_id":"102"}],"type":"journal_article","keyword":["Computational Mathematics","Algebra and Number Theory"],"publication":"Journal of Symbolic Computation","abstract":[{"text":"Given a field extension K/k of degree n we are interested in finding the subfields of K containing k. There can be more than polynomially many subfields. We introduce the notion of generating subfields, a set of up to n subfields whose intersections give the rest. We provide an efficient algorithm which uses linear algebra in k or lattice reduction along with factorization in any extension of K. Implementations show that previously difficult cases can now be handled.","lang":"eng"}],"publisher":"Elsevier BV","_id":"34846","page":"17-34","volume":52,"user_id":"93826","status":"public","citation":{"ieee":"M. van Hoeij, J. Klüners, and A. Novocin, “Generating subfields,” <i>Journal of Symbolic Computation</i>, vol. 52, pp. 17–34, 2011, doi: <a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">10.1016/j.jsc.2012.05.010</a>.","apa":"van Hoeij, M., Klüners, J., &#38; Novocin, A. (2011). Generating subfields. <i>Journal of Symbolic Computation</i>, <i>52</i>, 17–34. <a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">https://doi.org/10.1016/j.jsc.2012.05.010</a>","short":"M. van Hoeij, J. Klüners, A. Novocin, Journal of Symbolic Computation 52 (2011) 17–34.","chicago":"Hoeij, Mark van, Jürgen Klüners, and Andrew Novocin. “Generating Subfields.” <i>Journal of Symbolic Computation</i> 52 (2011): 17–34. <a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">https://doi.org/10.1016/j.jsc.2012.05.010</a>.","mla":"van Hoeij, Mark, et al. “Generating Subfields.” <i>Journal of Symbolic Computation</i>, vol. 52, Elsevier BV, 2011, pp. 17–34, doi:<a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">10.1016/j.jsc.2012.05.010</a>.","bibtex":"@article{van Hoeij_Klüners_Novocin_2011, title={Generating subfields}, volume={52}, DOI={<a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">10.1016/j.jsc.2012.05.010</a>}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={van Hoeij, Mark and Klüners, Jürgen and Novocin, Andrew}, year={2011}, pages={17–34} }","ama":"van Hoeij M, Klüners J, Novocin A. Generating subfields. <i>Journal of Symbolic Computation</i>. 2011;52:17-34. doi:<a href=\"https://doi.org/10.1016/j.jsc.2012.05.010\">10.1016/j.jsc.2012.05.010</a>"}},{"abstract":[{"lang":"eng","text":"This paper classifies the maximal finite subgroups of SP₂ₙ(Q) for 1⩽n⩽11 up to GL₂ₙ(Q) conjugacy in ."}],"extern":"1","publication":"Experimental Mathematics","issue":"2","department":[{"_id":"102"}],"type":"journal_article","keyword":["General Mathematics"],"date_created":"2023-03-07T08:36:46Z","intvolume":"        20","date_updated":"2023-04-04T09:24:42Z","publication_status":"published","publication_identifier":{"issn":["1058-6458","1944-950X"]},"author":[{"id":"82258","full_name":"Kirschmer, Markus","last_name":"Kirschmer","first_name":"Markus"}],"title":"Finite Symplectic Matrix Groups","year":"2011","doi":"10.1080/10586458.2011.564964","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Kirschmer_2011, title={Finite Symplectic Matrix Groups}, volume={20}, DOI={<a href=\"https://doi.org/10.1080/10586458.2011.564964\">10.1080/10586458.2011.564964</a>}, number={2}, journal={Experimental Mathematics}, publisher={Informa UK Limited}, author={Kirschmer, Markus}, year={2011}, pages={217–228} }","ama":"Kirschmer M. Finite Symplectic Matrix Groups. <i>Experimental Mathematics</i>. 2011;20(2):217-228. doi:<a href=\"https://doi.org/10.1080/10586458.2011.564964\">10.1080/10586458.2011.564964</a>","mla":"Kirschmer, Markus. “Finite Symplectic Matrix Groups.” <i>Experimental Mathematics</i>, vol. 20, no. 2, Informa UK Limited, 2011, pp. 217–28, doi:<a href=\"https://doi.org/10.1080/10586458.2011.564964\">10.1080/10586458.2011.564964</a>.","chicago":"Kirschmer, Markus. “Finite Symplectic Matrix Groups.” <i>Experimental Mathematics</i> 20, no. 2 (2011): 217–28. <a href=\"https://doi.org/10.1080/10586458.2011.564964\">https://doi.org/10.1080/10586458.2011.564964</a>.","short":"M. Kirschmer, Experimental Mathematics 20 (2011) 217–228.","ieee":"M. Kirschmer, “Finite Symplectic Matrix Groups,” <i>Experimental Mathematics</i>, vol. 20, no. 2, pp. 217–228, 2011, doi: <a href=\"https://doi.org/10.1080/10586458.2011.564964\">10.1080/10586458.2011.564964</a>.","apa":"Kirschmer, M. (2011). Finite Symplectic Matrix Groups. <i>Experimental Mathematics</i>, <i>20</i>(2), 217–228. <a href=\"https://doi.org/10.1080/10586458.2011.564964\">https://doi.org/10.1080/10586458.2011.564964</a>"},"status":"public","volume":20,"user_id":"93826","publisher":"Informa UK Limited","_id":"42798","page":"217-228"},{"status":"public","user_id":"93826","volume":172,"page":"2035-2104","publisher":"Annals of Mathematics","_id":"34886","citation":{"short":"É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” <i>Annals of Mathematics</i> 172, no. 3 (2010): 2035–2104. <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">https://doi.org/10.4007/annals.2010.172.2035</a>.","ieee":"É. Fouvry and J. Klüners, “On the negative Pell equation,” <i>Annals of Mathematics</i>, vol. 172, no. 3, pp. 2035–2104, 2010, doi: <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>.","apa":"Fouvry, É., &#38; Klüners, J. (2010). On the negative Pell equation. <i>Annals of Mathematics</i>, <i>172</i>(3), 2035–2104. <a href=\"https://doi.org/10.4007/annals.2010.172.2035\">https://doi.org/10.4007/annals.2010.172.2035</a>","bibtex":"@article{Fouvry_Klüners_2010, title={On the negative Pell equation}, volume={172}, DOI={<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>}, number={3}, journal={Annals of Mathematics}, publisher={Annals of Mathematics}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={2035–2104} }","ama":"Fouvry É, Klüners J. On the negative Pell equation. <i>Annals of Mathematics</i>. 2010;172(3):2035-2104. doi:<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Negative Pell Equation.” <i>Annals of Mathematics</i>, vol. 172, no. 3, Annals of Mathematics, 2010, pp. 2035–104, doi:<a href=\"https://doi.org/10.4007/annals.2010.172.2035\">10.4007/annals.2010.172.2035</a>."},"publication_status":"published","date_updated":"2023-03-06T09:50:37Z","intvolume":"       172","year":"2010","title":"On the negative Pell equation","publication_identifier":{"issn":["0003-486X"]},"author":[{"first_name":"Étienne","last_name":"Fouvry","full_name":"Fouvry, Étienne"},{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"}],"doi":"10.4007/annals.2010.172.2035","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We give asymptotic upper and lower bounds for the number of squarefree d (0 < d ≤ X) such that the equation x² − dy²= −1 is solvable. These estimates, as usual, can equivalently be interpreted in terms of real quadratic fields with a fundamental unit with norm −1 and give strong evidence in the direction of a conjecture due to P. Stevenhagen."}],"publication":"Annals of Mathematics","issue":"3","type":"journal_article","keyword":["Statistics","Probability and Uncertainty","Mathematics (miscellaneous)"],"department":[{"_id":"102"}],"date_created":"2022-12-23T09:09:02Z"},{"issue":"2","publication":"Proceedings of the London Mathematical Society","related_material":{"link":[{"relation":"confirmation","url":"https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=fc7ab412993fd2bf0069de42fbef1ecc69137755"}]},"abstract":[{"text":"We call a positive square-free integer d special, if d is not divisible by primes congruent to 3 mod 4. We show that the period of the expansion of in continued fractions is asymptotically more often odd than even, when we restrict to special integers. We note that this period is always even for a non-special square-free integer d. It is well known that the above period is odd if and only if the negative Pell equation x²−dy²=−1 is solvable. The latter problem is solvable if and only if the narrow and the ordinary class groups of ℚ(√d) are equal. In a prior work we fully described the asymptotics of the 4-ranks of those class groups. Here we get the first non-trivial results about the asymptotic behavior of the 8-rank of the narrow class group. For example, we show that more than 76% of the quadratic fields ℚ(√d), where d is special, have the property that the 8-rank of the narrow class group is zero.","lang":"eng"}],"date_created":"2022-12-23T09:22:49Z","keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"102"}],"title":"The parity of the period of the continued fraction of d","year":"2010","publication_identifier":{"issn":["0024-6115"]},"author":[{"full_name":"Fouvry, Étienne","first_name":"Étienne","last_name":"Fouvry"},{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"}],"date_updated":"2023-03-06T10:16:54Z","publication_status":"published","intvolume":"       101","language":[{"iso":"eng"}],"doi":"10.1112/plms/pdp057","citation":{"mla":"Fouvry, Étienne, and Jürgen Klüners. “The Parity of the Period of the Continued Fraction of d.” <i>Proceedings of the London Mathematical Society</i>, vol. 101, no. 2, Wiley, 2010, pp. 337–91, doi:<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>.","ama":"Fouvry É, Klüners J. The parity of the period of the continued fraction of d. <i>Proceedings of the London Mathematical Society</i>. 2010;101(2):337-391. doi:<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>","bibtex":"@article{Fouvry_Klüners_2010, title={The parity of the period of the continued fraction of d}, volume={101}, DOI={<a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>}, number={2}, journal={Proceedings of the London Mathematical Society}, publisher={Wiley}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={337–391} }","apa":"Fouvry, É., &#38; Klüners, J. (2010). The parity of the period of the continued fraction of d. <i>Proceedings of the London Mathematical Society</i>, <i>101</i>(2), 337–391. <a href=\"https://doi.org/10.1112/plms/pdp057\">https://doi.org/10.1112/plms/pdp057</a>","ieee":"É. Fouvry and J. Klüners, “The parity of the period of the continued fraction of d,” <i>Proceedings of the London Mathematical Society</i>, vol. 101, no. 2, pp. 337–391, 2010, doi: <a href=\"https://doi.org/10.1112/plms/pdp057\">10.1112/plms/pdp057</a>.","short":"É. Fouvry, J. Klüners, Proceedings of the London Mathematical Society 101 (2010) 337–391.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “The Parity of the Period of the Continued Fraction of d.” <i>Proceedings of the London Mathematical Society</i> 101, no. 2 (2010): 337–91. <a href=\"https://doi.org/10.1112/plms/pdp057\">https://doi.org/10.1112/plms/pdp057</a>."},"status":"public","page":"337-391","publisher":"Wiley","_id":"34888","user_id":"93826","volume":101},{"language":[{"iso":"eng"}],"doi":"10.2140/ant.2010.4.493","title":"On the Spiegelungssatz for the 4-rank","year":"2010","author":[{"full_name":"Fouvry, Étienne","first_name":"Étienne","last_name":"Fouvry"},{"id":"21202","last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"}],"publication_identifier":{"issn":["1937-0652"]},"date_updated":"2023-03-06T10:18:14Z","publication_status":"published","intvolume":"         4","date_created":"2022-12-23T09:10:12Z","type":"journal_article","keyword":["Algebra and Number Theory"],"department":[{"_id":"102"}],"publication":"Algebra &amp; Number Theory","issue":"5","abstract":[{"text":"Let d be a nonsquare positive integer. We give the value of the natural probability that the narrow ideal class groups of the quadratic fields ℚ(√d) and ℚ(√−d) have the same 4-ranks. ","lang":"eng"}],"page":"493-508","_id":"34887","publisher":"Mathematical Sciences Publishers","user_id":"93826","volume":4,"status":"public","citation":{"ieee":"É. Fouvry and J. Klüners, “On the Spiegelungssatz for the 4-rank,” <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, pp. 493–508, 2010, doi: <a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>.","apa":"Fouvry, É., &#38; Klüners, J. (2010). On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp; Number Theory</i>, <i>4</i>(5), 493–508. <a href=\"https://doi.org/10.2140/ant.2010.4.493\">https://doi.org/10.2140/ant.2010.4.493</a>","short":"É. Fouvry, J. Klüners, Algebra &#38;amp; Number Theory 4 (2010) 493–508.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.” <i>Algebra &#38;amp; Number Theory</i> 4, no. 5 (2010): 493–508. <a href=\"https://doi.org/10.2140/ant.2010.4.493\">https://doi.org/10.2140/ant.2010.4.493</a>.","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the Spiegelungssatz for the 4-Rank.” <i>Algebra &#38;amp; Number Theory</i>, vol. 4, no. 5, Mathematical Sciences Publishers, 2010, pp. 493–508, doi:<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>.","bibtex":"@article{Fouvry_Klüners_2010, title={On the Spiegelungssatz for the 4-rank}, volume={4}, DOI={<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>}, number={5}, journal={Algebra &#38;amp; Number Theory}, publisher={Mathematical Sciences Publishers}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2010}, pages={493–508} }","ama":"Fouvry É, Klüners J. On the Spiegelungssatz for the 4-rank. <i>Algebra &#38;amp; Number Theory</i>. 2010;4(5):493-508. doi:<a href=\"https://doi.org/10.2140/ant.2010.4.493\">10.2140/ant.2010.4.493</a>"}},{"status":"public","page":"1714-1747","_id":"42803","publisher":"Society for Industrial & Applied Mathematics (SIAM)","user_id":"93826","volume":39,"citation":{"mla":"Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” <i>SIAM Journal on Computing</i>, vol. 39, no. 5, Society for Industrial &#38; Applied Mathematics (SIAM), 2010, pp. 1714–47, doi:<a href=\"https://doi.org/10.1137/080734467\">10.1137/080734467</a>.","bibtex":"@article{Kirschmer_Voight_2010, title={Algorithmic Enumeration of Ideal Classes for Quaternion Orders}, volume={39}, DOI={<a href=\"https://doi.org/10.1137/080734467\">10.1137/080734467</a>}, number={5}, journal={SIAM Journal on Computing}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Kirschmer, Markus and Voight, John}, year={2010}, pages={1714–1747} }","ama":"Kirschmer M, Voight J. Algorithmic Enumeration of Ideal Classes for Quaternion Orders. <i>SIAM Journal on Computing</i>. 2010;39(5):1714-1747. doi:<a href=\"https://doi.org/10.1137/080734467\">10.1137/080734467</a>","ieee":"M. Kirschmer and J. Voight, “Algorithmic Enumeration of Ideal Classes for Quaternion Orders,” <i>SIAM Journal on Computing</i>, vol. 39, no. 5, pp. 1714–1747, 2010, doi: <a href=\"https://doi.org/10.1137/080734467\">10.1137/080734467</a>.","apa":"Kirschmer, M., &#38; Voight, J. (2010). Algorithmic Enumeration of Ideal Classes for Quaternion Orders. <i>SIAM Journal on Computing</i>, <i>39</i>(5), 1714–1747. <a href=\"https://doi.org/10.1137/080734467\">https://doi.org/10.1137/080734467</a>","chicago":"Kirschmer, Markus, and John Voight. “Algorithmic Enumeration of Ideal Classes for Quaternion Orders.” <i>SIAM Journal on Computing</i> 39, no. 5 (2010): 1714–47. <a href=\"https://doi.org/10.1137/080734467\">https://doi.org/10.1137/080734467</a>.","short":"M. Kirschmer, J. Voight, SIAM Journal on Computing 39 (2010) 1714–1747."},"year":"2010","title":"Algorithmic Enumeration of Ideal Classes for Quaternion Orders","publication_identifier":{"issn":["0097-5397","1095-7111"]},"author":[{"first_name":"Markus","last_name":"Kirschmer","full_name":"Kirschmer, Markus","id":"82258"},{"full_name":"Voight, John","last_name":"Voight","first_name":"John"}],"publication_status":"published","date_updated":"2023-04-04T09:25:08Z","intvolume":"        39","language":[{"iso":"eng"}],"doi":"10.1137/080734467","publication":"SIAM Journal on Computing","issue":"5","extern":"1","abstract":[{"text":"We provide algorithms to count and enumerate representatives of the (right) ideal classes of an Eichler order in a quaternion algebra defined over a number field. We analyze the run time of these algorithms and consider several related problems, including the computation of two-sided ideal classes, isomorphism classes of orders, connecting ideals for orders, and ideal principalization. We conclude by giving the complete list of definite Eichler orders with class number at most 2.","lang":"eng"}],"date_created":"2023-03-07T08:49:35Z","type":"journal_article","keyword":["General Mathematics","General Computer Science"],"department":[{"_id":"102"}]},{"abstract":[{"lang":"eng","text":"We prove that van Hoeij’s original algorithm to factor univariate polynomials over the rationals runs in polynomial time, as well as natural variants. In particular, our approach also yields polynomial time complexity results for bivariate polynomials over a finite field."}],"publication":"Journal de Théorie des Nombres de Bordeaux","issue":"1","type":"journal_article","keyword":["Algebra and Number Theory"],"department":[{"_id":"102"}],"date_created":"2022-12-23T09:33:37Z","publication_status":"published","date_updated":"2023-03-06T09:09:56Z","intvolume":"        21","title":"Factoring polynomials over global fields","year":"2009","publication_identifier":{"issn":["1246-7405"]},"author":[{"last_name":"Belabas","first_name":"Karim","full_name":"Belabas, Karim"},{"last_name":"van Hoeij","first_name":"Mark","full_name":"van Hoeij, Mark"},{"id":"21202","last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"},{"first_name":"Allan","last_name":"Steel","full_name":"Steel, Allan"}],"doi":"10.5802/jtnb.655","language":[{"iso":"eng"}],"citation":{"short":"K. Belabas, M. van Hoeij, J. Klüners, A. Steel, Journal de Théorie Des Nombres de Bordeaux 21 (2009) 15–39.","chicago":"Belabas, Karim, Mark van Hoeij, Jürgen Klüners, and Allan Steel. “Factoring Polynomials over Global Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 21, no. 1 (2009): 15–39. <a href=\"https://doi.org/10.5802/jtnb.655\">https://doi.org/10.5802/jtnb.655</a>.","apa":"Belabas, K., van Hoeij, M., Klüners, J., &#38; Steel, A. (2009). Factoring polynomials over global fields. <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>21</i>(1), 15–39. <a href=\"https://doi.org/10.5802/jtnb.655\">https://doi.org/10.5802/jtnb.655</a>","ieee":"K. Belabas, M. van Hoeij, J. Klüners, and A. Steel, “Factoring polynomials over global fields,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 21, no. 1, pp. 15–39, 2009, doi: <a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>.","ama":"Belabas K, van Hoeij M, Klüners J, Steel A. Factoring polynomials over global fields. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2009;21(1):15-39. doi:<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>","bibtex":"@article{Belabas_van Hoeij_Klüners_Steel_2009, title={Factoring polynomials over global fields}, volume={21}, DOI={<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>}, number={1}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Belabas, Karim and van Hoeij, Mark and Klüners, Jürgen and Steel, Allan}, year={2009}, pages={15–39} }","mla":"Belabas, Karim, et al. “Factoring Polynomials over Global Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 21, no. 1, Cellule MathDoc/CEDRAM, 2009, pp. 15–39, doi:<a href=\"https://doi.org/10.5802/jtnb.655\">10.5802/jtnb.655</a>."},"external_id":{"arxiv":["math/0409510 "]},"status":"public","user_id":"93826","volume":21,"page":"15-39","_id":"34889","publisher":"Cellule MathDoc/CEDRAM"},{"abstract":[{"lang":"eng","text":"In this survey, we report about a new algorithm for factoring polynomials due to Mark van Hoeij. The main idea is that the combinatorial problem that occurs in the Zassenhaus algorithm is reduced to a very special knapsack problem. In case of rational polynomials, this knapsack problem can be very efficiently solved by the LLL algorithm. This gives a polynomial time algorithm, which also works very well in practice."}],"related_material":{"link":[{"url":"https://www.researchgate.net/profile/Juergen-Klueners/publication/226764840_The_van_Hoeij_Algorithm_for_Factoring_Polynomials/links/00463532f2216a64ae000000/The-van-Hoeij-Algorithm-for-Factoring-Polynomials.pdf?origin=publication_detail","relation":"confirmation"}]},"citation":{"mla":"Klüners, Jürgen. “The van Hoeij Algorithm for Factoring Polynomials.” <i>The LLL Algorithm</i>, Springer Berlin Heidelberg, 2009, doi:<a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">10.1007/978-3-642-02295-1_8</a>.","ama":"Klüners J. The van Hoeij Algorithm for Factoring Polynomials. In: <i>The LLL Algorithm</i>. Springer Berlin Heidelberg; 2009. doi:<a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">10.1007/978-3-642-02295-1_8</a>","bibtex":"@inbook{Klüners_2009, place={Berlin, Heidelberg}, title={The van Hoeij Algorithm for Factoring Polynomials}, DOI={<a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">10.1007/978-3-642-02295-1_8</a>}, booktitle={The LLL Algorithm}, publisher={Springer Berlin Heidelberg}, author={Klüners, Jürgen}, year={2009} }","apa":"Klüners, J. (2009). The van Hoeij Algorithm for Factoring Polynomials. In <i>The LLL Algorithm</i>. Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">https://doi.org/10.1007/978-3-642-02295-1_8</a>","ieee":"J. Klüners, “The van Hoeij Algorithm for Factoring Polynomials,” in <i>The LLL Algorithm</i>, Berlin, Heidelberg: Springer Berlin Heidelberg, 2009.","short":"J. Klüners, in: The LLL Algorithm, Springer Berlin Heidelberg, Berlin, Heidelberg, 2009.","chicago":"Klüners, Jürgen. “The van Hoeij Algorithm for Factoring Polynomials.” In <i>The LLL Algorithm</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. <a href=\"https://doi.org/10.1007/978-3-642-02295-1_8\">https://doi.org/10.1007/978-3-642-02295-1_8</a>."},"publication":"The LLL Algorithm","department":[{"_id":"102"}],"type":"book_chapter","place":"Berlin, Heidelberg","date_created":"2023-01-11T09:48:17Z","date_updated":"2023-03-06T09:10:34Z","publication_status":"published","author":[{"id":"21202","last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"}],"publication_identifier":{"isbn":["9783642022944","9783642022951"],"issn":["1619-7100"]},"title":"The van Hoeij Algorithm for Factoring Polynomials","year":"2009","status":"public","doi":"10.1007/978-3-642-02295-1_8","user_id":"93826","publisher":"Springer Berlin Heidelberg","_id":"35959","language":[{"iso":"eng"}]},{"citation":{"mla":"Kirschmer, Markus. <i>Finite Symplectic Matrix Groups (Dissertation)</i>. 2009.","bibtex":"@book{Kirschmer_2009, place={RWTH Aachen University}, title={Finite symplectic matrix groups (Dissertation)}, author={Kirschmer, Markus}, year={2009} }","ama":"Kirschmer M. <i>Finite Symplectic Matrix Groups (Dissertation)</i>.; 2009.","ieee":"M. Kirschmer, <i>Finite symplectic matrix groups (Dissertation)</i>. RWTH Aachen University, 2009.","apa":"Kirschmer, M. (2009). <i>Finite symplectic matrix groups (Dissertation)</i>.","chicago":"Kirschmer, Markus. <i>Finite Symplectic Matrix Groups (Dissertation)</i>. RWTH Aachen University, 2009.","short":"M. Kirschmer, Finite Symplectic Matrix Groups (Dissertation), RWTH Aachen University, 2009."},"extern":"1","abstract":[{"text":"Die invarianten Formen aus dem Anhang sind hier verfügbar:http://www.math.rwth-aachen.de/homes/Markus.Kirschmer/symplectic/","lang":"eng"}],"date_created":"2023-04-11T08:03:29Z","place":"RWTH Aachen University","department":[{"_id":"102"}],"type":"dissertation","author":[{"id":"82258","full_name":"Kirschmer, Markus","first_name":"Markus","last_name":"Kirschmer"}],"title":"Finite symplectic matrix groups (Dissertation)","year":"2009","status":"public","date_updated":"2023-04-11T08:14:10Z","_id":"43453","language":[{"iso":"eng"}],"page":"149","user_id":"93826"},{"status":"public","page":"1-26","_id":"34895","publisher":"Walter de Gruyter GmbH","user_id":"93826","volume":2004,"citation":{"mla":"Klüners, Jürgen, and G. Malle. “Counting Nilpotent Galois Extensions.” <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i>, vol. 2004, no. 572, Walter de Gruyter GmbH, 2006, pp. 1–26, doi:<a href=\"https://doi.org/10.1515/crll.2004.050\">10.1515/crll.2004.050</a>.","bibtex":"@article{Klüners_Malle_2006, title={Counting nilpotent Galois extensions}, volume={2004}, DOI={<a href=\"https://doi.org/10.1515/crll.2004.050\">10.1515/crll.2004.050</a>}, number={572}, journal={Journal für die reine und angewandte Mathematik (Crelles Journal)}, publisher={Walter de Gruyter GmbH}, author={Klüners, Jürgen and Malle, G.}, year={2006}, pages={1–26} }","ama":"Klüners J, Malle G. Counting nilpotent Galois extensions. <i>Journal für die reine und angewandte Mathematik (Crelles Journal)</i>. 2006;2004(572):1-26. doi:<a href=\"https://doi.org/10.1515/crll.2004.050\">10.1515/crll.2004.050</a>","ieee":"J. Klüners and G. Malle, “Counting nilpotent Galois extensions,” <i>Journal für die reine und angewandte Mathematik (Crelles Journal)</i>, vol. 2004, no. 572, pp. 1–26, 2006, doi: <a href=\"https://doi.org/10.1515/crll.2004.050\">10.1515/crll.2004.050</a>.","apa":"Klüners, J., &#38; Malle, G. (2006). Counting nilpotent Galois extensions. <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i>, <i>2004</i>(572), 1–26. <a href=\"https://doi.org/10.1515/crll.2004.050\">https://doi.org/10.1515/crll.2004.050</a>","short":"J. Klüners, G. Malle, Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2004 (2006) 1–26.","chicago":"Klüners, Jürgen, and G. Malle. “Counting Nilpotent Galois Extensions.” <i>Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)</i> 2004, no. 572 (2006): 1–26. <a href=\"https://doi.org/10.1515/crll.2004.050\">https://doi.org/10.1515/crll.2004.050</a>."},"external_id":{"arxiv":["math/0112318"]},"title":"Counting nilpotent Galois extensions","year":"2006","author":[{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"},{"first_name":"G.","last_name":"Malle","full_name":"Malle, G."}],"publication_identifier":{"issn":["0075-4102","1435-5345"]},"publication_status":"published","date_updated":"2023-03-06T09:11:16Z","intvolume":"      2004","language":[{"iso":"eng"}],"doi":"10.1515/crll.2004.050","issue":"572","publication":"Journal für die reine und angewandte Mathematik (Crelles Journal)","abstract":[{"text":"We obtain strong information on the asymptotic behaviour of the counting function for nilpotent Galois extensions with bounded discriminant of arbitrary number fields. This extends previous investigations for the case of abelian groups. In particular, the result confirms a conjecture by the second author on this function for arbitrary groups in the nilpotent case. We further prove compatibility of the conjecture with taking wreath products with the cyclic group of order 2 and give examples in degree up to 8. ","lang":"eng"}],"date_created":"2022-12-23T09:50:49Z","type":"journal_article","keyword":["Applied Mathematics","General Mathematics"],"department":[{"_id":"102"}]},{"doi":"10.5802/jtnb.561","language":[{"iso":"eng"}],"date_updated":"2023-03-06T09:12:04Z","publication_status":"published","intvolume":"        18","title":"Asymptotics of number fields and the Cohen–Lenstra heuristics","year":"2006","publication_identifier":{"issn":["1246-7405"]},"author":[{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"}],"keyword":["Algebra and Number Theory"],"type":"journal_article","department":[{"_id":"102"}],"date_created":"2022-12-23T09:37:01Z","abstract":[{"lang":"eng","text":"We study the asymptotics conjecture of Malle for dihedral groups Dℓ of order 2ℓ, where ℓ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds. "}],"publication":"Journal de Théorie des Nombres de Bordeaux","issue":"3","user_id":"93826","volume":18,"page":"607-615","publisher":"Cellule MathDoc/CEDRAM","_id":"34891","status":"public","external_id":{"arxiv":["math/0512260 "]},"citation":{"mla":"Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.” <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 18, no. 3, Cellule MathDoc/CEDRAM, 2006, pp. 607–15, doi:<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>.","ama":"Klüners J. Asymptotics of number fields and the Cohen–Lenstra heuristics. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2006;18(3):607-615. doi:<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>","bibtex":"@article{Klüners_2006, title={Asymptotics of number fields and the Cohen–Lenstra heuristics}, volume={18}, DOI={<a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>}, number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule MathDoc/CEDRAM}, author={Klüners, Jürgen}, year={2006}, pages={607–615} }","apa":"Klüners, J. (2006). Asymptotics of number fields and the Cohen–Lenstra heuristics. <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>18</i>(3), 607–615. <a href=\"https://doi.org/10.5802/jtnb.561\">https://doi.org/10.5802/jtnb.561</a>","ieee":"J. Klüners, “Asymptotics of number fields and the Cohen–Lenstra heuristics,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 18, no. 3, pp. 607–615, 2006, doi: <a href=\"https://doi.org/10.5802/jtnb.561\">10.5802/jtnb.561</a>.","short":"J. Klüners, Journal de Théorie Des Nombres de Bordeaux 18 (2006) 607–615.","chicago":"Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 18, no. 3 (2006): 607–15. <a href=\"https://doi.org/10.5802/jtnb.561\">https://doi.org/10.5802/jtnb.561</a>."}},{"status":"public","volume":167,"user_id":"93826","publisher":"Springer Science and Business Media LLC","_id":"34890","page":"455-513","citation":{"apa":"Fouvry, É., &#38; Klüners, J. (2006). On the 4-rank of class groups of quadratic number fields. <i>Inventiones Mathematicae</i>, <i>167</i>(3), 455–513. <a href=\"https://doi.org/10.1007/s00222-006-0021-2\">https://doi.org/10.1007/s00222-006-0021-2</a>","ieee":"É. Fouvry and J. Klüners, “On the 4-rank of class groups of quadratic number fields,” <i>Inventiones mathematicae</i>, vol. 167, no. 3, pp. 455–513, 2006, doi: <a href=\"https://doi.org/10.1007/s00222-006-0021-2\">10.1007/s00222-006-0021-2</a>.","short":"É. Fouvry, J. Klüners, Inventiones Mathematicae 167 (2006) 455–513.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “On the 4-Rank of Class Groups of Quadratic Number Fields.” <i>Inventiones Mathematicae</i> 167, no. 3 (2006): 455–513. <a href=\"https://doi.org/10.1007/s00222-006-0021-2\">https://doi.org/10.1007/s00222-006-0021-2</a>.","mla":"Fouvry, Étienne, and Jürgen Klüners. “On the 4-Rank of Class Groups of Quadratic Number Fields.” <i>Inventiones Mathematicae</i>, vol. 167, no. 3, Springer Science and Business Media LLC, 2006, pp. 455–513, doi:<a href=\"https://doi.org/10.1007/s00222-006-0021-2\">10.1007/s00222-006-0021-2</a>.","ama":"Fouvry É, Klüners J. On the 4-rank of class groups of quadratic number fields. <i>Inventiones mathematicae</i>. 2006;167(3):455-513. doi:<a href=\"https://doi.org/10.1007/s00222-006-0021-2\">10.1007/s00222-006-0021-2</a>","bibtex":"@article{Fouvry_Klüners_2006, title={On the 4-rank of class groups of quadratic number fields}, volume={167}, DOI={<a href=\"https://doi.org/10.1007/s00222-006-0021-2\">10.1007/s00222-006-0021-2</a>}, number={3}, journal={Inventiones mathematicae}, publisher={Springer Science and Business Media LLC}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2006}, pages={455–513} }"},"intvolume":"       167","publication_status":"published","date_updated":"2023-03-06T09:12:30Z","publication_identifier":{"issn":["0020-9910","1432-1297"]},"author":[{"full_name":"Fouvry, Étienne","first_name":"Étienne","last_name":"Fouvry"},{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"}],"title":"On the 4-rank of class groups of quadratic number fields","year":"2006","doi":"10.1007/s00222-006-0021-2","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We prove that the 4-rank of class groups of quadratic number fields behaves as predicted in an extension due to Gerth of the Cohen–Lenstra heuristics. "}],"related_material":{"link":[{"relation":"confirmation","url":"https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/ranks.pdf"}]},"issue":"3","publication":"Inventiones mathematicae","department":[{"_id":"102"}],"type":"journal_article","keyword":["General Mathematics"],"date_created":"2022-12-23T09:36:15Z"},{"publisher":"Springer Berlin Heidelberg","_id":"35958","language":[{"iso":"eng"}],"user_id":"93826","doi":"10.1007/11792086_4","publication_identifier":{"isbn":["9783540360759","9783540360766"],"issn":["0302-9743","1611-3349"]},"author":[{"first_name":"Étienne","last_name":"Fouvry","full_name":"Fouvry, Étienne"},{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"}],"title":"Cohen–Lenstra Heuristics of Quadratic Number Fields","status":"public","year":"2006","publication_status":"published","date_updated":"2023-03-06T09:13:15Z","date_created":"2023-01-11T09:46:47Z","place":"Berlin, Heidelberg","department":[{"_id":"102"}],"type":"book_chapter","citation":{"ama":"Fouvry É, Klüners J. Cohen–Lenstra Heuristics of Quadratic Number Fields. In: <i>Lecture Notes in Computer Science</i>. Springer Berlin Heidelberg; 2006. doi:<a href=\"https://doi.org/10.1007/11792086_4\">10.1007/11792086_4</a>","bibtex":"@inbook{Fouvry_Klüners_2006, place={Berlin, Heidelberg}, title={Cohen–Lenstra Heuristics of Quadratic Number Fields}, DOI={<a href=\"https://doi.org/10.1007/11792086_4\">10.1007/11792086_4</a>}, booktitle={Lecture Notes in Computer Science}, publisher={Springer Berlin Heidelberg}, author={Fouvry, Étienne and Klüners, Jürgen}, year={2006} }","mla":"Fouvry, Étienne, and Jürgen Klüners. “Cohen–Lenstra Heuristics of Quadratic Number Fields.” <i>Lecture Notes in Computer Science</i>, Springer Berlin Heidelberg, 2006, doi:<a href=\"https://doi.org/10.1007/11792086_4\">10.1007/11792086_4</a>.","short":"É. Fouvry, J. Klüners, in: Lecture Notes in Computer Science, Springer Berlin Heidelberg, Berlin, Heidelberg, 2006.","chicago":"Fouvry, Étienne, and Jürgen Klüners. “Cohen–Lenstra Heuristics of Quadratic Number Fields.” In <i>Lecture Notes in Computer Science</i>. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. <a href=\"https://doi.org/10.1007/11792086_4\">https://doi.org/10.1007/11792086_4</a>.","apa":"Fouvry, É., &#38; Klüners, J. (2006). Cohen–Lenstra Heuristics of Quadratic Number Fields. In <i>Lecture Notes in Computer Science</i>. Springer Berlin Heidelberg. <a href=\"https://doi.org/10.1007/11792086_4\">https://doi.org/10.1007/11792086_4</a>","ieee":"É. Fouvry and J. Klüners, “Cohen–Lenstra Heuristics of Quadratic Number Fields,” in <i>Lecture Notes in Computer Science</i>, Berlin, Heidelberg: Springer Berlin Heidelberg, 2006."},"publication":"Lecture Notes in Computer Science","abstract":[{"lang":"eng","text":"We establish a link between some heuristic asymptotic formulas (due to Cohen and Lenstra) concerning the moments of the p–part of the class groups of quadratic fields and formulas giving the frequency of the values of the p–rank of these class groups."}],"related_material":{"link":[{"url":"https://www.researchgate.net/profile/Juergen-Klueners/publication/221451567_Cohen-Lenstra_Heuristics_of_Quadratic_Number_Fields/links/0a85e53298eaed8777000000/Cohen-Lenstra-Heuristics-of-Quadratic-Number-Fields.pdf?origin=publication_detail","relation":"confirmation"}]}},{"title":"The number of S₄-fields with given discriminant","year":"2006","author":[{"id":"21202","last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen"}],"publication_identifier":{"issn":["0065-1036","1730-6264"]},"publication_status":"published","date_updated":"2023-03-06T09:52:41Z","intvolume":"       122","language":[{"iso":"eng"}],"doi":"10.4064/aa122-2-3","issue":"2","publication":"Acta Arithmetica","abstract":[{"lang":"eng","text":"We prove that the number of quartic S4--extensions of the rationals of given discriminant d is $O_\\eps(d^{1/2+\\eps})$ for all $\\eps>0$. For a prime number p we derive that the dimension of the space of octahedral modular forms of weight 1 and conductor p or p² is bounded above by O(p¹/²log(p)²). "}],"date_created":"2022-12-23T09:40:25Z","type":"journal_article","keyword":["Algebra and Number Theory"],"department":[{"_id":"102"}],"status":"public","page":"185-194","_id":"34892","publisher":"Institute of Mathematics, Polish Academy of Sciences","user_id":"93826","volume":122,"citation":{"ama":"Klüners J. The number of S₄-fields with given discriminant. <i>Acta Arithmetica</i>. 2006;122(2):185-194. doi:<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>","bibtex":"@article{Klüners_2006, title={The number of S₄-fields with given discriminant}, volume={122}, DOI={<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>}, number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish Academy of Sciences}, author={Klüners, Jürgen}, year={2006}, pages={185–194} }","mla":"Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta Arithmetica</i>, vol. 122, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2006, pp. 185–94, doi:<a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>.","chicago":"Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta Arithmetica</i> 122, no. 2 (2006): 185–94. <a href=\"https://doi.org/10.4064/aa122-2-3\">https://doi.org/10.4064/aa122-2-3</a>.","short":"J. Klüners, Acta Arithmetica 122 (2006) 185–194.","apa":"Klüners, J. (2006). The number of S₄-fields with given discriminant. <i>Acta Arithmetica</i>, <i>122</i>(2), 185–194. <a href=\"https://doi.org/10.4064/aa122-2-3\">https://doi.org/10.4064/aa122-2-3</a>","ieee":"J. Klüners, “The number of S₄-fields with given discriminant,” <i>Acta Arithmetica</i>, vol. 122, no. 2, pp. 185–194, 2006, doi: <a href=\"https://doi.org/10.4064/aa122-2-3\">10.4064/aa122-2-3</a>."},"external_id":{"arxiv":["math/0411484"]}},{"page":"411-414","publisher":"Elsevier BV","_id":"34894","user_id":"93826","volume":340,"status":"public","external_id":{"arxiv":["math/0411486 "]},"citation":{"ieee":"J. Klüners, “A counter example to Malle’s conjecture on the asymptotics of discriminants,” <i>Comptes Rendus Mathematique</i>, vol. 340, no. 6, pp. 411–414, 2005, doi: <a href=\"https://doi.org/10.1016/j.crma.2005.02.010\">10.1016/j.crma.2005.02.010</a>.","apa":"Klüners, J. (2005). A counter example to Malle’s conjecture on the asymptotics of discriminants. <i>Comptes Rendus Mathematique</i>, <i>340</i>(6), 411–414. <a href=\"https://doi.org/10.1016/j.crma.2005.02.010\">https://doi.org/10.1016/j.crma.2005.02.010</a>","chicago":"Klüners, Jürgen. “A Counter Example to Malle’s Conjecture on the Asymptotics of Discriminants.” <i>Comptes Rendus Mathematique</i> 340, no. 6 (2005): 411–14. <a href=\"https://doi.org/10.1016/j.crma.2005.02.010\">https://doi.org/10.1016/j.crma.2005.02.010</a>.","short":"J. Klüners, Comptes Rendus Mathematique 340 (2005) 411–414.","mla":"Klüners, Jürgen. “A Counter Example to Malle’s Conjecture on the Asymptotics of Discriminants.” <i>Comptes Rendus Mathematique</i>, vol. 340, no. 6, Elsevier BV, 2005, pp. 411–14, doi:<a href=\"https://doi.org/10.1016/j.crma.2005.02.010\">10.1016/j.crma.2005.02.010</a>.","bibtex":"@article{Klüners_2005, title={A counter example to Malle’s conjecture on the asymptotics of discriminants}, volume={340}, DOI={<a href=\"https://doi.org/10.1016/j.crma.2005.02.010\">10.1016/j.crma.2005.02.010</a>}, number={6}, journal={Comptes Rendus Mathematique}, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={2005}, pages={411–414} }","ama":"Klüners J. A counter example to Malle’s conjecture on the asymptotics of discriminants. <i>Comptes Rendus Mathematique</i>. 2005;340(6):411-414. doi:<a href=\"https://doi.org/10.1016/j.crma.2005.02.010\">10.1016/j.crma.2005.02.010</a>"},"language":[{"iso":"eng"}],"doi":"10.1016/j.crma.2005.02.010","title":"A counter example to Malle's conjecture on the asymptotics of discriminants","year":"2005","author":[{"full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen","id":"21202"}],"publication_identifier":{"issn":["1631-073X"]},"date_updated":"2023-03-06T09:15:10Z","publication_status":"published","intvolume":"       340","date_created":"2022-12-23T09:44:05Z","keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"102"}],"publication":"Comptes Rendus Mathematique","issue":"6","abstract":[{"lang":"eng","text":"In this Note we give a counter example to a conjecture of Malle which predicts the asymptotic behavior of the counting functions for field extensions with given Galois group and bounded discriminant. "}]}]