[{"doi":"10.5802/jtnb.655","date_updated":"2023-03-06T09:09:56Z","author":[{"first_name":"Karim","last_name":"Belabas","full_name":"Belabas, Karim"},{"full_name":"van Hoeij, Mark","last_name":"van Hoeij","first_name":"Mark"},{"first_name":"Jürgen","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"},{"first_name":"Allan","last_name":"Steel","full_name":"Steel, Allan"}],"volume":21,"citation":{"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>.","short":"K. Belabas, M. van Hoeij, J. Klüners, A. Steel, Journal de Théorie Des Nombres de Bordeaux 21 (2009) 15–39.","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} }","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>.","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>.","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>"},"intvolume":"        21","page":"15-39","publication_status":"published","publication_identifier":{"issn":["1246-7405"]},"_id":"34889","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","title":"Factoring polynomials over global fields","publisher":"Cellule MathDoc/CEDRAM","date_created":"2022-12-23T09:33:37Z","year":"2009","issue":"1","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["math/0409510 "]},"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"},{"publication":"The LLL Algorithm","type":"book_chapter","status":"public","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."}],"department":[{"_id":"102"}],"user_id":"93826","_id":"35959","language":[{"iso":"eng"}],"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"}]},"publication_identifier":{"issn":["1619-7100"],"isbn":["9783642022944","9783642022951"]},"publication_status":"published","citation":{"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} }","short":"J. Klüners, in: The LLL Algorithm, Springer Berlin Heidelberg, Berlin, Heidelberg, 2009.","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>.","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>","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>","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>.","ieee":"J. Klüners, “The van Hoeij Algorithm for Factoring Polynomials,” in <i>The LLL Algorithm</i>, Berlin, Heidelberg: Springer Berlin Heidelberg, 2009."},"place":"Berlin, Heidelberg","year":"2009","author":[{"first_name":"Jürgen","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"}],"date_created":"2023-01-11T09:48:17Z","date_updated":"2023-03-06T09:10:34Z","publisher":"Springer Berlin Heidelberg","doi":"10.1007/978-3-642-02295-1_8","title":"The van Hoeij Algorithm for Factoring Polynomials"},{"abstract":[{"lang":"eng","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. "}],"publication":"Journal für die reine und angewandte Mathematik (Crelles Journal)","keyword":["Applied Mathematics","General Mathematics"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["math/0112318"]},"year":"2006","issue":"572","title":"Counting nilpotent Galois extensions","publisher":"Walter de Gruyter GmbH","date_created":"2022-12-23T09:50:49Z","status":"public","type":"journal_article","_id":"34895","user_id":"93826","department":[{"_id":"102"}],"citation":{"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.","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>","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>.","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>."},"page":"1-26","intvolume":"      2004","publication_status":"published","publication_identifier":{"issn":["0075-4102","1435-5345"]},"doi":"10.1515/crll.2004.050","date_updated":"2023-03-06T09:11:16Z","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"},{"last_name":"Malle","full_name":"Malle, G.","first_name":"G."}],"volume":2004},{"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"external_id":{"arxiv":["math/0512260 "]},"abstract":[{"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. ","lang":"eng"}],"publication":"Journal de Théorie des Nombres de Bordeaux","title":"Asymptotics of number fields and the Cohen–Lenstra heuristics","date_created":"2022-12-23T09:37:01Z","publisher":"Cellule MathDoc/CEDRAM","year":"2006","issue":"3","department":[{"_id":"102"}],"user_id":"93826","_id":"34891","status":"public","type":"journal_article","doi":"10.5802/jtnb.561","volume":18,"author":[{"first_name":"Jürgen","id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners"}],"date_updated":"2023-03-06T09:12:04Z","intvolume":"        18","page":"607-615","citation":{"short":"J. Klüners, Journal de Théorie Des Nombres de Bordeaux 18 (2006) 607–615.","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>.","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>","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>","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>.","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>."},"publication_identifier":{"issn":["1246-7405"]},"publication_status":"published"},{"type":"journal_article","status":"public","_id":"34890","user_id":"93826","department":[{"_id":"102"}],"publication_status":"published","publication_identifier":{"issn":["0020-9910","1432-1297"]},"related_material":{"link":[{"url":"https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/ranks.pdf","relation":"confirmation"}]},"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>","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} }","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>.","short":"É. Fouvry, J. Klüners, Inventiones Mathematicae 167 (2006) 455–513.","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>","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>.","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>."},"page":"455-513","intvolume":"       167","date_updated":"2023-03-06T09:12:30Z","author":[{"last_name":"Fouvry","full_name":"Fouvry, Étienne","first_name":"Étienne"},{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"}],"volume":167,"doi":"10.1007/s00222-006-0021-2","publication":"Inventiones mathematicae","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. "}],"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"issue":"3","year":"2006","publisher":"Springer Science and Business Media LLC","date_created":"2022-12-23T09:36:15Z","title":"On the 4-rank of class groups of quadratic number fields"},{"publication":"Lecture Notes in Computer Science","type":"book_chapter","status":"public","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"102"}],"user_id":"93826","_id":"35958","language":[{"iso":"eng"}],"related_material":{"link":[{"relation":"confirmation","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"}]},"publication_identifier":{"isbn":["9783540360759","9783540360766"],"issn":["0302-9743","1611-3349"]},"publication_status":"published","citation":{"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} }","short":"É. Fouvry, J. Klüners, in: Lecture Notes in Computer Science, Springer Berlin Heidelberg, Berlin, Heidelberg, 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>.","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>","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>.","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.","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>"},"place":"Berlin, Heidelberg","year":"2006","date_created":"2023-01-11T09:46:47Z","author":[{"last_name":"Fouvry","full_name":"Fouvry, Étienne","first_name":"Étienne"},{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"date_updated":"2023-03-06T09:13:15Z","publisher":"Springer Berlin Heidelberg","doi":"10.1007/11792086_4","title":"Cohen–Lenstra Heuristics of Quadratic Number Fields"},{"external_id":{"arxiv":["math/0411484"]},"language":[{"iso":"eng"}],"keyword":["Algebra and Number Theory"],"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","publisher":"Institute of Mathematics, Polish Academy of Sciences","title":"The number of S₄-fields with given discriminant","issue":"2","year":"2006","user_id":"93826","department":[{"_id":"102"}],"_id":"34892","type":"journal_article","status":"public","author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"volume":122,"date_updated":"2023-03-06T09:52:41Z","doi":"10.4064/aa122-2-3","publication_status":"published","publication_identifier":{"issn":["0065-1036","1730-6264"]},"citation":{"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>","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>.","short":"J. Klüners, Acta Arithmetica 122 (2006) 185–194.","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>.","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>.","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>"},"intvolume":"       122","page":"185-194"},{"type":"journal_article","status":"public","_id":"34894","user_id":"93826","department":[{"_id":"102"}],"publication_status":"published","publication_identifier":{"issn":["1631-073X"]},"citation":{"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>","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>.","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>.","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>.","short":"J. Klüners, Comptes Rendus Mathematique 340 (2005) 411–414.","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} }","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>"},"page":"411-414","intvolume":"       340","date_updated":"2023-03-06T09:15:10Z","author":[{"id":"21202","full_name":"Klüners, Jürgen","last_name":"Klüners","first_name":"Jürgen"}],"volume":340,"doi":"10.1016/j.crma.2005.02.010","publication":"Comptes Rendus Mathematique","abstract":[{"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. ","lang":"eng"}],"external_id":{"arxiv":["math/0411486 "]},"keyword":["General Mathematics"],"language":[{"iso":"eng"}],"issue":"6","year":"2005","publisher":"Elsevier BV","date_created":"2022-12-23T09:44:05Z","title":"A counter example to Malle's conjecture on the asymptotics of discriminants"},{"doi":"10.1016/j.jalgebra.2005.04.013","date_updated":"2023-03-06T09:55:09Z","author":[{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"},{"first_name":"Sebastian","last_name":"Pauli","full_name":"Pauli, Sebastian"}],"volume":292,"citation":{"chicago":"Klüners, Jürgen, and Sebastian Pauli. “Computing Residue Class Rings and Picard Groups of Orders.” <i>Journal of Algebra</i> 292, no. 1 (2005): 47–64. <a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">https://doi.org/10.1016/j.jalgebra.2005.04.013</a>.","ieee":"J. Klüners and S. Pauli, “Computing residue class rings and Picard groups of orders,” <i>Journal of Algebra</i>, vol. 292, no. 1, pp. 47–64, 2005, doi: <a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">10.1016/j.jalgebra.2005.04.013</a>.","ama":"Klüners J, Pauli S. Computing residue class rings and Picard groups of orders. <i>Journal of Algebra</i>. 2005;292(1):47-64. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">10.1016/j.jalgebra.2005.04.013</a>","apa":"Klüners, J., &#38; Pauli, S. (2005). Computing residue class rings and Picard groups of orders. <i>Journal of Algebra</i>, <i>292</i>(1), 47–64. <a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">https://doi.org/10.1016/j.jalgebra.2005.04.013</a>","mla":"Klüners, Jürgen, and Sebastian Pauli. “Computing Residue Class Rings and Picard Groups of Orders.” <i>Journal of Algebra</i>, vol. 292, no. 1, Elsevier BV, 2005, pp. 47–64, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">10.1016/j.jalgebra.2005.04.013</a>.","bibtex":"@article{Klüners_Pauli_2005, title={Computing residue class rings and Picard groups of orders}, volume={292}, DOI={<a href=\"https://doi.org/10.1016/j.jalgebra.2005.04.013\">10.1016/j.jalgebra.2005.04.013</a>}, number={1}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Klüners, Jürgen and Pauli, Sebastian}, year={2005}, pages={47–64} }","short":"J. Klüners, S. Pauli, Journal of Algebra 292 (2005) 47–64."},"intvolume":"       292","page":"47-64","publication_status":"published","publication_identifier":{"issn":["0021-8693"]},"_id":"34893","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","title":"Computing residue class rings and Picard groups of orders","publisher":"Elsevier BV","date_created":"2022-12-23T09:41:06Z","year":"2005","issue":"1","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Let K be a global field and O be an order of K. We develop algorithms for the computation of the unit group of residue class rings for ideals O in . As an application we show how to compute the unit group and the Picard group of O provided that we are able to compute the unit group and class group of the maximal order O of K."}],"publication":"Journal of Algebra"},{"title":"Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)","publisher":"Shaker Verlag","date_updated":"2023-04-11T08:13:38Z","date_created":"2023-03-07T09:05:29Z","author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"}],"year":"2005","place":"Universiät Kassel","citation":{"bibtex":"@book{Klüners_2005, place={Universiät Kassel}, title={Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)}, publisher={Shaker Verlag}, author={Klüners, Jürgen}, year={2005} }","mla":"Klüners, Jürgen. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Shaker Verlag, 2005.","short":"J. Klüners, Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation), Shaker Verlag, Universiät Kassel, 2005.","apa":"Klüners, J. (2005). <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Shaker Verlag.","chicago":"Klüners, Jürgen. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Universiät Kassel: Shaker Verlag, 2005.","ieee":"J. Klüners, <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Universiät Kassel: Shaker Verlag, 2005.","ama":"Klüners J. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)</i>. Shaker Verlag; 2005."},"page":"114","publication_identifier":{"isbn":["978-3-8322-4003-5"]},"extern":"1","language":[{"iso":"ger"}],"_id":"42807","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"misc"},{"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"abstract":[{"text":"We apply class field theory to the computation of the minimal discriminants for certain solvable groups. In particular, we apply our techniques to small Frobenius groups and all imprimitive degree 8 groups such that the corresponding fields have only a degree 2 and no degree 4 subfield.","lang":"eng"}],"publication":"Journal of Number Theory","title":"Minimal discriminants for fields with small Frobenius groups as Galois groups","publisher":"Elsevier BV","date_created":"2022-12-23T09:53:23Z","year":"2003","issue":"2","_id":"34896","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","doi":"10.1016/s0022-314x(02)00071-9","date_updated":"2023-03-06T09:19:16Z","author":[{"full_name":"Fieker, Claus","last_name":"Fieker","first_name":"Claus"},{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"volume":99,"citation":{"ieee":"C. Fieker and J. Klüners, “Minimal discriminants for fields with small Frobenius groups as Galois groups,” <i>Journal of Number Theory</i>, vol. 99, no. 2, pp. 318–337, 2003, doi: <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>.","chicago":"Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i> 99, no. 2 (2003): 318–37. <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">https://doi.org/10.1016/s0022-314x(02)00071-9</a>.","ama":"Fieker C, Klüners J. Minimal discriminants for fields with small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>. 2003;99(2):318-337. doi:<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>","short":"C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337.","bibtex":"@article{Fieker_Klüners_2003, title={Minimal discriminants for fields with small Frobenius groups as Galois groups}, volume={99}, DOI={<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>}, number={2}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Fieker, Claus and Klüners, Jürgen}, year={2003}, pages={318–337} }","mla":"Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i>, vol. 99, no. 2, Elsevier BV, 2003, pp. 318–37, doi:<a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">10.1016/s0022-314x(02)00071-9</a>.","apa":"Fieker, C., &#38; Klüners, J. (2003). Minimal discriminants for fields with small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>, <i>99</i>(2), 318–337. <a href=\"https://doi.org/10.1016/s0022-314x(02)00071-9\">https://doi.org/10.1016/s0022-314x(02)00071-9</a>"},"page":"318-337","intvolume":"        99","publication_status":"published","publication_identifier":{"issn":["0022-314X"]}},{"abstract":[{"text":"Let {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t \\!}) be a finite extension. We describe algorithms for computing subfields and automorphisms of {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t }\\!). As an application we give an algorithm for finding decompositions of rational functions in {\\small \\ℚ(α)}. We also present an algorithm which decides if an extension {\\ASIE L}\\,/{\\small \\ℚ}({\\ASIE t \\!}) is a subfield of {\\ASIE K}. In case [{\\ASIE K : \\;}{\\small\\ℚ}({\\ASIE t \\!})] = [{\\ASIE L : \\;}{\\small \\ℚ}({\\ASIE t \\!})] we obtain a {\\small \\ℚ}({\\ASIE t \\!})-isomorphism test. Furthermore, we describe an algorithm which computes subfields of the normal closure of {\\ASIE K}\\,/{\\small \\ℚ}({\\ASIE t \\!}).","lang":"eng"}],"publication":"Experiment. Math. ","language":[{"iso":"eng"}],"keyword":["algorithms","decompositions","Galois groups","subfields"],"year":"2002","issue":"2","title":"Algorithms for function fields","date_created":"2023-01-11T09:45:40Z","publisher":"Elsevier BV","status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"35954","page":"171-181","intvolume":"        11","citation":{"ama":"Klüners J. Algorithms for function fields. <i>Experiment Math </i>. 2002;11(2):171-181.","ieee":"J. Klüners, “Algorithms for function fields,” <i>Experiment. Math. </i>, vol. 11, no. 2, pp. 171–181, 2002.","chicago":"Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i> 11, no. 2 (2002): 171–81.","bibtex":"@article{Klüners_2002, title={Algorithms for function fields}, volume={11}, number={2}, journal={Experiment. Math. }, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={2002}, pages={171–181} }","short":"J. Klüners, Experiment. Math.  11 (2002) 171–181.","mla":"Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i>, vol. 11, no. 2, Elsevier BV, 2002, pp. 171–81.","apa":"Klüners, J. (2002). Algorithms for function fields. <i>Experiment. Math. </i>, <i>11</i>(2), 171–181."},"related_material":{"link":[{"relation":"confirmation","url":"https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-2/Algorithms-for-function-fields/em/1062621213.full"}]},"publication_status":"published","volume":11,"author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"date_updated":"2023-03-06T10:26:58Z"},{"date_created":"2022-12-23T09:56:22Z","publisher":"Wiley","title":"A Database for Field Extensions of the Rationals","year":"2001","external_id":{"arxiv":["math/0102232"]},"language":[{"iso":"eng"}],"keyword":["Computational Theory and Mathematics","General Mathematics"],"publication":"LMS Journal of Computation and Mathematics","abstract":[{"lang":"eng","text":"This paper announces the creation of a database for number fields. It describes the contents and the methods of access, indicates the origin of the polynomials, and formulates the aims of this collection of fields."}],"volume":4,"author":[{"first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202"},{"first_name":"Gunter","last_name":"Malle","full_name":"Malle, Gunter"}],"date_updated":"2023-03-02T09:53:08Z","doi":"10.1112/s1461157000000851","publication_identifier":{"issn":["1461-1570"]},"publication_status":"published","intvolume":"         4","page":"182-196","citation":{"chicago":"Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of the Rationals.” <i>LMS Journal of Computation and Mathematics</i> 4 (2001): 182–96. <a href=\"https://doi.org/10.1112/s1461157000000851\">https://doi.org/10.1112/s1461157000000851</a>.","ieee":"J. Klüners and G. Malle, “A Database for Field Extensions of the Rationals,” <i>LMS Journal of Computation and Mathematics</i>, vol. 4, pp. 182–196, 2001, doi: <a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>.","ama":"Klüners J, Malle G. A Database for Field Extensions of the Rationals. <i>LMS Journal of Computation and Mathematics</i>. 2001;4:182-196. doi:<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>","apa":"Klüners, J., &#38; Malle, G. (2001). A Database for Field Extensions of the Rationals. <i>LMS Journal of Computation and Mathematics</i>, <i>4</i>, 182–196. <a href=\"https://doi.org/10.1112/s1461157000000851\">https://doi.org/10.1112/s1461157000000851</a>","bibtex":"@article{Klüners_Malle_2001, title={A Database for Field Extensions of the Rationals}, volume={4}, DOI={<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Klüners, Jürgen and Malle, Gunter}, year={2001}, pages={182–196} }","short":"J. Klüners, G. Malle, LMS Journal of Computation and Mathematics 4 (2001) 182–196.","mla":"Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of the Rationals.” <i>LMS Journal of Computation and Mathematics</i>, vol. 4, Wiley, 2001, pp. 182–96, doi:<a href=\"https://doi.org/10.1112/s1461157000000851\">10.1112/s1461157000000851</a>."},"department":[{"_id":"102"}],"user_id":"93826","_id":"34897","type":"journal_article","status":"public"},{"publication_identifier":{"issn":["0747-7171"]},"publication_status":"published","intvolume":"        30","page":"653-674","citation":{"apa":"Geissler, K., &#38; Klüners, J. (2000). Galois Group Computation for Rational Polynomials. <i>Journal of Symbolic Computation</i>, <i>30</i>(6), 653–674. <a href=\"https://doi.org/10.1006/jsco.2000.0377\">https://doi.org/10.1006/jsco.2000.0377</a>","bibtex":"@article{Geissler_Klüners_2000, title={Galois Group Computation for Rational Polynomials}, volume={30}, DOI={<a href=\"https://doi.org/10.1006/jsco.2000.0377\">10.1006/jsco.2000.0377</a>}, number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Geissler, Katharina and Klüners, Jürgen}, year={2000}, pages={653–674} }","short":"K. Geissler, J. Klüners, Journal of Symbolic Computation 30 (2000) 653–674.","mla":"Geissler, Katharina, and Jürgen Klüners. “Galois Group Computation for Rational Polynomials.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, Elsevier BV, 2000, pp. 653–74, doi:<a href=\"https://doi.org/10.1006/jsco.2000.0377\">10.1006/jsco.2000.0377</a>.","ieee":"K. Geissler and J. Klüners, “Galois Group Computation for Rational Polynomials,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp. 653–674, 2000, doi: <a href=\"https://doi.org/10.1006/jsco.2000.0377\">10.1006/jsco.2000.0377</a>.","chicago":"Geissler, Katharina, and Jürgen Klüners. “Galois Group Computation for Rational Polynomials.” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000): 653–74. <a href=\"https://doi.org/10.1006/jsco.2000.0377\">https://doi.org/10.1006/jsco.2000.0377</a>.","ama":"Geissler K, Klüners J. Galois Group Computation for Rational Polynomials. <i>Journal of Symbolic Computation</i>. 2000;30(6):653-674. doi:<a href=\"https://doi.org/10.1006/jsco.2000.0377\">10.1006/jsco.2000.0377</a>"},"volume":30,"author":[{"full_name":"Geissler, Katharina","last_name":"Geissler","first_name":"Katharina"},{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"date_updated":"2023-03-06T09:58:06Z","doi":"10.1006/jsco.2000.0377","type":"journal_article","status":"public","department":[{"_id":"102"}],"user_id":"93826","_id":"34900","issue":"6","year":"2000","date_created":"2022-12-23T09:58:16Z","publisher":"Elsevier BV","title":"Galois Group Computation for Rational Polynomials","publication":"Journal of Symbolic Computation","abstract":[{"text":"We describe methods for the computation of Galois groups of univariate polynomials over the rationals which we have implemented up to degree 15. These methods are based on Stauduhar’s algorithm. All computations are done in unramified p -adic extensions. For imprimitive groups we give an improvement using subfields. In the primitive case we use known subgroups of the Galois group together with a combination of Stauduhar’s method and the absolute resolvent method.","lang":"eng"}],"language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"]},{"keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"publication":"Journal of Symbolic Computation","abstract":[{"text":"Let L = K(α) be an Abelian extension of degree n of a number field K, given by the minimal polynomial of α over K. We describe an algorithm for computing the local Artin map associated with the extension L / K at a finite or infinite prime v of K. We apply this algorithm to decide if a nonzero a ∈ K is a norm from L, assuming that L / K is cyclic.","lang":"eng"}],"publisher":"Elsevier BV","date_created":"2022-12-23T09:58:48Z","title":"Computing Local Artin Maps, and Solvability of Norm Equations","issue":"3","year":"2000","_id":"34901","user_id":"93826","department":[{"_id":"102"}],"type":"journal_article","status":"public","date_updated":"2023-03-06T09:57:34Z","author":[{"last_name":"Acciaro","full_name":"Acciaro, Vincenzo","first_name":"Vincenzo"},{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"volume":30,"doi":"10.1006/jsco.2000.0361","publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"citation":{"apa":"Acciaro, V., &#38; Klüners, J. (2000). Computing Local Artin Maps, and Solvability of Norm Equations. <i>Journal of Symbolic Computation</i>, <i>30</i>(3), 239–252. <a href=\"https://doi.org/10.1006/jsco.2000.0361\">https://doi.org/10.1006/jsco.2000.0361</a>","bibtex":"@article{Acciaro_Klüners_2000, title={Computing Local Artin Maps, and Solvability of Norm Equations}, volume={30}, DOI={<a href=\"https://doi.org/10.1006/jsco.2000.0361\">10.1006/jsco.2000.0361</a>}, number={3}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Acciaro, Vincenzo and Klüners, Jürgen}, year={2000}, pages={239–252} }","short":"V. Acciaro, J. Klüners, Journal of Symbolic Computation 30 (2000) 239–252.","mla":"Acciaro, Vincenzo, and Jürgen Klüners. “Computing Local Artin Maps, and Solvability of Norm Equations.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 3, Elsevier BV, 2000, pp. 239–52, doi:<a href=\"https://doi.org/10.1006/jsco.2000.0361\">10.1006/jsco.2000.0361</a>.","ama":"Acciaro V, Klüners J. Computing Local Artin Maps, and Solvability of Norm Equations. <i>Journal of Symbolic Computation</i>. 2000;30(3):239-252. doi:<a href=\"https://doi.org/10.1006/jsco.2000.0361\">10.1006/jsco.2000.0361</a>","chicago":"Acciaro, Vincenzo, and Jürgen Klüners. “Computing Local Artin Maps, and Solvability of Norm Equations.” <i>Journal of Symbolic Computation</i> 30, no. 3 (2000): 239–52. <a href=\"https://doi.org/10.1006/jsco.2000.0361\">https://doi.org/10.1006/jsco.2000.0361</a>.","ieee":"V. Acciaro and J. Klüners, “Computing Local Artin Maps, and Solvability of Norm Equations,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 3, pp. 239–252, 2000, doi: <a href=\"https://doi.org/10.1006/jsco.2000.0361\">10.1006/jsco.2000.0361</a>."},"intvolume":"        30","page":"239-252"},{"_id":"34899","user_id":"93826","department":[{"_id":"102"}],"status":"public","type":"journal_article","doi":"10.1006/jsco.2000.0378","date_updated":"2023-03-06T10:48:05Z","author":[{"last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen"},{"full_name":"Malle, Gunter","last_name":"Malle","first_name":"Gunter"}],"volume":30,"citation":{"ama":"Klüners J, Malle G. Explicit Galois Realization of Transitive Groups of Degree up to 15. <i>Journal of Symbolic Computation</i>. 2000;30(6):675-716. doi:<a href=\"https://doi.org/10.1006/jsco.2000.0378\">10.1006/jsco.2000.0378</a>","ieee":"J. Klüners and G. Malle, “Explicit Galois Realization of Transitive Groups of Degree up to 15,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp. 675–716, 2000, doi: <a href=\"https://doi.org/10.1006/jsco.2000.0378\">10.1006/jsco.2000.0378</a>.","chicago":"Klüners, Jürgen, and Gunter Malle. “Explicit Galois Realization of Transitive Groups of Degree up to 15.” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000): 675–716. <a href=\"https://doi.org/10.1006/jsco.2000.0378\">https://doi.org/10.1006/jsco.2000.0378</a>.","bibtex":"@article{Klüners_Malle_2000, title={Explicit Galois Realization of Transitive Groups of Degree up to 15}, volume={30}, DOI={<a href=\"https://doi.org/10.1006/jsco.2000.0378\">10.1006/jsco.2000.0378</a>}, number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Klüners, Jürgen and Malle, Gunter}, year={2000}, pages={675–716} }","mla":"Klüners, Jürgen, and Gunter Malle. “Explicit Galois Realization of Transitive Groups of Degree up to 15.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, Elsevier BV, 2000, pp. 675–716, doi:<a href=\"https://doi.org/10.1006/jsco.2000.0378\">10.1006/jsco.2000.0378</a>.","short":"J. Klüners, G. Malle, Journal of Symbolic Computation 30 (2000) 675–716.","apa":"Klüners, J., &#38; Malle, G. (2000). Explicit Galois Realization of Transitive Groups of Degree up to 15. <i>Journal of Symbolic Computation</i>, <i>30</i>(6), 675–716. <a href=\"https://doi.org/10.1006/jsco.2000.0378\">https://doi.org/10.1006/jsco.2000.0378</a>"},"intvolume":"        30","page":"675-716","publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"keyword":["Computational Mathematics","Algebra and Number Theory"],"language":[{"iso":"eng"}],"abstract":[{"text":"We describe methods for the construction of polynomials with certain types of Galois groups. As an application we deduce that all transitive groups G up to degree 15 occur as Galois groups of regular extensions of ℚ (t), and in each case compute a polynomial f ∈ ℚ [ x ] with Gal(f)  = G.","lang":"eng"}],"publication":"Journal of Symbolic Computation","title":"Explicit Galois Realization of Transitive Groups of Degree up to 15","publisher":"Elsevier BV","date_created":"2022-12-23T09:57:28Z","year":"2000","issue":"6"},{"status":"public","type":"journal_article","user_id":"93826","department":[{"_id":"102"}],"_id":"34898","citation":{"ama":"Klüners J. A Polynomial with Galois GroupSL2(11). <i>Journal of Symbolic Computation</i>. 2000;30(6):733-737. doi:<a href=\"https://doi.org/10.1006/jsco.2000.0380\">10.1006/jsco.2000.0380</a>","chicago":"Klüners, Jürgen. “A Polynomial with Galois GroupSL2(11).” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000): 733–37. <a href=\"https://doi.org/10.1006/jsco.2000.0380\">https://doi.org/10.1006/jsco.2000.0380</a>.","ieee":"J. Klüners, “A Polynomial with Galois GroupSL2(11),” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp. 733–737, 2000, doi: <a href=\"https://doi.org/10.1006/jsco.2000.0380\">10.1006/jsco.2000.0380</a>.","bibtex":"@article{Klüners_2000, title={A Polynomial with Galois GroupSL2(11)}, volume={30}, DOI={<a href=\"https://doi.org/10.1006/jsco.2000.0380\">10.1006/jsco.2000.0380</a>}, number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={2000}, pages={733–737} }","short":"J. Klüners, Journal of Symbolic Computation 30 (2000) 733–737.","mla":"Klüners, Jürgen. “A Polynomial with Galois GroupSL2(11).” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, Elsevier BV, 2000, pp. 733–37, doi:<a href=\"https://doi.org/10.1006/jsco.2000.0380\">10.1006/jsco.2000.0380</a>.","apa":"Klüners, J. (2000). A Polynomial with Galois GroupSL2(11). <i>Journal of Symbolic Computation</i>, <i>30</i>(6), 733–737. <a href=\"https://doi.org/10.1006/jsco.2000.0380\">https://doi.org/10.1006/jsco.2000.0380</a>"},"intvolume":"        30","page":"733-737","publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"doi":"10.1006/jsco.2000.0380","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"volume":30,"date_updated":"2023-03-06T10:48:40Z","abstract":[{"lang":"eng","text":"We compute a polynomial with Galois group SL₂(11) over ℚ. Furthermore we prove that SL₂(11) is the Galois group of a regular extension of ℚ (t)."}],"publication":"Journal of Symbolic Computation","language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"year":"2000","issue":"6","title":"A Polynomial with Galois GroupSL2(11)","date_created":"2022-12-23T09:56:52Z","publisher":"Elsevier BV"},{"user_id":"93826","department":[{"_id":"102"}],"_id":"34902","type":"journal_article","status":"public","author":[{"first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners"}],"volume":27,"date_updated":"2023-03-06T09:21:29Z","doi":"10.1006/jsco.1998.0252","publication_status":"published","publication_identifier":{"issn":["0747-7171"]},"citation":{"apa":"Klüners, J. (1999). On Polynomial Decompositions. <i>Journal of Symbolic Computation</i>, <i>27</i>(3), 261–269. <a href=\"https://doi.org/10.1006/jsco.1998.0252\">https://doi.org/10.1006/jsco.1998.0252</a>","mla":"Klüners, Jürgen. “On Polynomial Decompositions.” <i>Journal of Symbolic Computation</i>, vol. 27, no. 3, Elsevier BV, 1999, pp. 261–69, doi:<a href=\"https://doi.org/10.1006/jsco.1998.0252\">10.1006/jsco.1998.0252</a>.","short":"J. Klüners, Journal of Symbolic Computation 27 (1999) 261–269.","bibtex":"@article{Klüners_1999, title={On Polynomial Decompositions}, volume={27}, DOI={<a href=\"https://doi.org/10.1006/jsco.1998.0252\">10.1006/jsco.1998.0252</a>}, number={3}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={1999}, pages={261–269} }","ama":"Klüners J. On Polynomial Decompositions. <i>Journal of Symbolic Computation</i>. 1999;27(3):261-269. doi:<a href=\"https://doi.org/10.1006/jsco.1998.0252\">10.1006/jsco.1998.0252</a>","chicago":"Klüners, Jürgen. “On Polynomial Decompositions.” <i>Journal of Symbolic Computation</i> 27, no. 3 (1999): 261–69. <a href=\"https://doi.org/10.1006/jsco.1998.0252\">https://doi.org/10.1006/jsco.1998.0252</a>.","ieee":"J. Klüners, “On Polynomial Decompositions,” <i>Journal of Symbolic Computation</i>, vol. 27, no. 3, pp. 261–269, 1999, doi: <a href=\"https://doi.org/10.1006/jsco.1998.0252\">10.1006/jsco.1998.0252</a>."},"page":"261-269","intvolume":"        27","language":[{"iso":"eng"}],"keyword":["Computational Mathematics","Algebra and Number Theory"],"publication":"Journal of Symbolic Computation","abstract":[{"text":"We present a new polynomial decomposition which generalizes the functional and homogeneous bivariate decomposition of irreducible monic polynomials in one variable over the rationals. With these decompositions it is possible to calculate the roots of an imprimitive polynomial by solving polynomial equations of lower degree.","lang":"eng"}],"date_created":"2022-12-23T10:01:15Z","publisher":"Elsevier BV","title":"On Polynomial Decompositions","issue":"3","year":"1999"},{"status":"public","type":"journal_article","department":[{"_id":"102"}],"user_id":"93826","_id":"35941","intvolume":"        68","page":"1179-1186","citation":{"apa":"Klüners, J., &#38; Acciaro, V. (1999). Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>, <i>68</i>(227), 1179–1186.","mla":"Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” <i>Mathematics of Computation</i>, vol. 68, no. 227, American Mathematical Society (AMS), 1999, pp. 1179–86.","bibtex":"@article{Klüners_Acciaro_1999, title={Computing Automorphisms of Abelian Number Fields}, volume={68}, number={227}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Acciaro, Vincenzo}, year={1999}, pages={1179–1186} }","short":"J. Klüners, V. Acciaro, Mathematics of Computation 68 (1999) 1179–1186.","chicago":"Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” <i>Mathematics of Computation</i> 68, no. 227 (1999): 1179–86.","ieee":"J. Klüners and V. Acciaro, “Computing Automorphisms of Abelian Number Fields,” <i>Mathematics of Computation</i>, vol. 68, no. 227, pp. 1179–1186, 1999.","ama":"Klüners J, Acciaro V. Computing Automorphisms of Abelian Number Fields. <i>Mathematics of Computation</i>. 1999;68(227):1179-1186."},"related_material":{"link":[{"url":"https://www.ams.org/journals/mcom/1999-68-227/S0025-5718-99-01084-4/S0025-5718-99-01084-4.pdf","relation":"confirmation"}]},"publication_identifier":{"issn":["1088-6842","0025-5718"]},"publication_status":"published","volume":68,"author":[{"full_name":"Klüners, Jürgen","id":"21202","last_name":"Klüners","first_name":"Jürgen"},{"full_name":"Acciaro, Vincenzo","last_name":"Acciaro","first_name":"Vincenzo"}],"date_updated":"2023-03-06T10:28:52Z","abstract":[{"text":"Let L = ℚ(α) be an abelian number field of degree n. Most\r\nalgorithms for computing the lattice of subfields of L require the computation\r\nof all the conjugates of α. This is usually achieved by factoring the minimal\r\npolynomial mα(x) of α over L. In practice, the existing algorithms for factoring\r\npolynomials over algebraic number fields can handle only problems of moderate\r\nsize. In this paper we describe a fast probabilistic algorithm for computing\r\nthe conjugates of α, which is based on p-adic techniques. Given mα(x) and a\r\nrational prime p which does not divide the discriminant disc(mα(x)) of mα(x),\r\nthe algorithm computes the Frobenius automorphism of p in time polynomial\r\nin the size of p and in the size of mα(x). By repeatedly applying the algorithm\r\nto randomly chosen primes it is possible to compute all the conjugates of α.","lang":"eng"}],"publication":"Mathematics of Computation","language":[{"iso":"eng"}],"year":"1999","issue":"227","title":"Computing Automorphisms of Abelian Number Fields","date_created":"2023-01-11T09:31:21Z","publisher":"American Mathematical Society (AMS)"},{"language":[{"iso":"eng"}],"user_id":"93826","_id":"34905","status":"public","abstract":[{"text":"Let ℚ(α) be an algebraic number field given by the\r\nminimal polynomial f of α. We want to determine all subfields\r\nℚ(β) ⊂ Q(α) of given degree. It is convenient to describe each\r\nsubfield by a pair (g, h) ∈ Z [t] x ℚ[t] such that g is the minimal\r\npolynomial of β = h(α) . There is a bijection between the block\r\nsystems of the Galois group of f and the subfields of ℚ(α). These\r\nblock systems are computed using cyclic subgroups of the Galois\r\ngroup which we get from the Dedekind criterion. When a block\r\nsystem is known we compute the corresponding subfield using p-\r\nadic methods. We give a detailed description for all parts of the\r\nalgorithm.","lang":"eng"}],"publication":"Journal de Theorie des Nombres de Bordeaux","type":"journal_article","doi":"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0","title":"On computing subfields. A detailed description of the algorithm ","volume":10,"date_created":"2022-12-23T10:24:43Z","author":[{"last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen"}],"date_updated":"2023-03-06T10:34:22Z","publisher":"Elsevier BV","page":"243-271","intvolume":"        10","citation":{"short":"J. Klüners, Journal de Theorie Des Nombres de Bordeaux 10 (1998) 243–271.","mla":"Klüners, Jürgen. “On Computing Subfields. A Detailed Description of the Algorithm .” <i>Journal de Theorie Des Nombres de Bordeaux</i>, vol. 10, no. 2, Elsevier BV, 1998, pp. 243–71, doi:<a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>.","bibtex":"@article{Klüners_1998, title={On computing subfields. A detailed description of the algorithm }, volume={10}, DOI={<a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>}, number={2}, journal={Journal de Theorie des Nombres de Bordeaux}, publisher={Elsevier BV}, author={Klüners, Jürgen}, year={1998}, pages={243–271} }","apa":"Klüners, J. (1998). On computing subfields. A detailed description of the algorithm . <i>Journal de Theorie Des Nombres de Bordeaux</i>, <i>10</i>(2), 243–271. <a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>","ama":"Klüners J. On computing subfields. A detailed description of the algorithm . <i>Journal de Theorie des Nombres de Bordeaux</i>. 1998;10(2):243-271. doi:<a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>","ieee":"J. Klüners, “On computing subfields. A detailed description of the algorithm ,” <i>Journal de Theorie des Nombres de Bordeaux</i>, vol. 10, no. 2, pp. 243–271, 1998, doi: <a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>.","chicago":"Klüners, Jürgen. “On Computing Subfields. A Detailed Description of the Algorithm .” <i>Journal de Theorie Des Nombres de Bordeaux</i> 10, no. 2 (1998): 243–71. <a href=\"https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0\">https://jtnb.centre-mersenne.org/item/?id=JTNB_1998__10_2_243_0</a>."},"year":"1998","related_material":{"link":[{"relation":"confirmation","url":"http://www.numdam.org/item/JTNB_1998__10_2_243_0/"}]},"issue":"2","publication_status":"published"}]