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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>"},"status":"public","page":"3618-3656","publisher":"Oxford University Press (OUP)","_id":"34885","user_id":"93826","volume":2011,"publication":"International Mathematics Research Notices","issue":"16","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."}],"date_created":"2022-12-23T09:08:00Z","keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"102"}],"year":"2011","title":"Weighted Distribution of the 4-rank of Class Groups and Applications","publication_identifier":{"issn":["1687-0247","1073-7928"]},"author":[{"full_name":"Fouvry, Étienne","first_name":"Étienne","last_name":"Fouvry"},{"last_name":"Klüners","first_name":"Jürgen","full_name":"Klüners, Jürgen","id":"21202"}],"date_updated":"2023-03-06T09:07:46Z","publication_status":"published","intvolume":"      2011","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnq223"},{"department":[{"_id":"102"}],"type":"journal_article","keyword":["Computational Mathematics","Algebra and Number Theory"],"date_created":"2022-12-22T10:54:15Z","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"}],"publication":"Journal of Symbolic Computation","doi":"10.1016/j.jsc.2012.05.010","language":[{"iso":"eng"}],"intvolume":"        52","date_updated":"2023-03-06T09:46:15Z","publication_status":"published","author":[{"first_name":"Mark","last_name":"van Hoeij","full_name":"van Hoeij, Mark"},{"id":"21202","full_name":"Klüners, Jürgen","first_name":"Jürgen","last_name":"Klüners"},{"first_name":"Andrew","last_name":"Novocin","full_name":"Novocin, Andrew"}],"publication_identifier":{"issn":["0747-7171"]},"title":"Generating subfields","year":"2011","citation":{"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>.","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>","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>","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>."},"volume":52,"user_id":"93826","publisher":"Elsevier BV","_id":"34846","page":"17-34","status":"public"},{"citation":{"ama":"Kirschmer M. 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Kirschmer, Experimental Mathematics 20 (2011) 217–228.","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>.","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>","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>."},"status":"public","user_id":"93826","volume":20,"page":"217-228","publisher":"Informa UK Limited","_id":"42798","extern":"1","abstract":[{"lang":"eng","text":"This paper classifies the maximal finite subgroups of SP₂ₙ(Q) for 1⩽n⩽11 up to GL₂ₙ(Q) conjugacy in ."}],"publication":"Experimental Mathematics","issue":"2","keyword":["General Mathematics"],"type":"journal_article","department":[{"_id":"102"}],"date_created":"2023-03-07T08:36:46Z","publication_status":"published","date_updated":"2023-04-04T09:24:42Z","intvolume":"        20","year":"2011","title":"Finite Symplectic Matrix Groups","author":[{"full_name":"Kirschmer, Markus","first_name":"Markus","last_name":"Kirschmer","id":"82258"}],"publication_identifier":{"issn":["1058-6458","1944-950X"]},"doi":"10.1080/10586458.2011.564964","language":[{"iso":"eng"}]},{"intvolume":"       351","date_updated":"2023-05-07T01:39:57Z","publication_status":"published","author":[{"full_name":"Burban, Igor","first_name":"Igor","last_name":"Burban","id":"72064"},{"last_name":"Drozd","first_name":"Yu.","full_name":"Drozd, Yu."}],"year":"2011","status":"public","title":"Tilting on non–commutative rational projective curves","volume":351,"user_id":"49063","_id":"44349","language":[{"iso":"eng"}],"page":"665–709","extern":"1","citation":{"chicago":"Burban, Igor, and Yu. 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Masdemont. “Spacecraft Trajectories to the L3 Point of the Sun–Earth Three-Body Problem.” <i>Celestial Mechanics and Dynamical Astronomy</i>, 2010, 215–32. <a href=\"https://doi.org/10.1007/s10569-010-9299-x\">https://doi.org/10.1007/s10569-010-9299-x</a>.","short":"M. Tantardini, E. Fantino, Y. Ren, P. Pergola, G. Gómez, J.J. Masdemont, Celestial Mechanics and Dynamical Astronomy (2010) 215–232.","apa":"Tantardini, M., Fantino, E., Ren, Y., Pergola, P., Gómez, G., &#38; Masdemont, J. J. (2010). Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem. <i>Celestial Mechanics and Dynamical Astronomy</i>, 215–232. <a href=\"https://doi.org/10.1007/s10569-010-9299-x\">https://doi.org/10.1007/s10569-010-9299-x</a>","ieee":"M. Tantardini, E. Fantino, Y. Ren, P. Pergola, G. Gómez, and J. J. 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