[{"citation":{"ieee":"M. Kirschmer and G. Nebe, “Quaternary quadratic lattices over number fields,” <i>International Journal of Number Theory</i>, vol. 15, no. 02, pp. 309–325, 2019, doi: <a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>.","apa":"Kirschmer, M., &#38; Nebe, G. (2019). Quaternary quadratic lattices over number fields. <i>International Journal of Number Theory</i>, <i>15</i>(02), 309–325. <a href=\"https://doi.org/10.1142/s1793042119500131\">https://doi.org/10.1142/s1793042119500131</a>","mla":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” <i>International Journal of Number Theory</i>, vol. 15, no. 02, World Scientific Pub Co Pte Lt, 2019, pp. 309–25, doi:<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>.","bibtex":"@article{Kirschmer_Nebe_2019, title={Quaternary quadratic lattices over number fields}, volume={15}, DOI={<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>}, number={02}, journal={International Journal of Number Theory}, publisher={World Scientific Pub Co Pte Lt}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2019}, pages={309–325} }","chicago":"Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number Fields.” <i>International Journal of Number Theory</i> 15, no. 02 (2019): 309–25. <a href=\"https://doi.org/10.1142/s1793042119500131\">https://doi.org/10.1142/s1793042119500131</a>.","short":"M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325.","ama":"Kirschmer M, Nebe G. Quaternary quadratic lattices over number fields. <i>International Journal of Number Theory</i>. 2019;15(02):309-325. doi:<a href=\"https://doi.org/10.1142/s1793042119500131\">10.1142/s1793042119500131</a>"},"publisher":"World Scientific Pub Co Pte Lt","_id":"34917","page":"309-325","volume":15,"user_id":"82258","status":"public","date_created":"2022-12-23T11:05:09Z","department":[{"_id":"102"}],"keyword":["Algebra and Number Theory"],"type":"journal_article","issue":"02","publication":"International Journal of Number Theory","abstract":[{"lang":"eng","text":"We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q)."}],"language":[{"iso":"eng"}],"doi":"10.1142/s1793042119500131","publication_identifier":{"issn":["1793-0421","1793-7310"]},"author":[{"id":"82258","first_name":"Markus","last_name":"Kirschmer","full_name":"Kirschmer, Markus"},{"first_name":"Gabriele","last_name":"Nebe","full_name":"Nebe, Gabriele"}],"year":"2019","title":"Quaternary quadratic lattices over number fields","intvolume":"        15","date_updated":"2023-12-06T10:05:59Z","publication_status":"published"},{"abstract":[{"lang":"eng","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. "}],"publication":"International Journal of Number Theory","issue":"03","type":"journal_article","department":[{"_id":"102"}],"date_created":"2022-12-22T10:55:47Z","date_updated":"2023-03-02T14:10:38Z","publication_status":"published","intvolume":"         8","year":"2012","title":"The Distribution of Number Fields with Wreath Products as Galois Groups ","author":[{"first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen","id":"21202"}],"publication_identifier":{"issn":["1793-0421","1793-7310"]},"doi":"10.1142/s1793042112500492","language":[{"iso":"eng"}],"citation":{"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>.","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>","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.","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>.","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} }","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>"},"external_id":{"arxiv":["1108.5597 "]},"status":"public","user_id":"21202","volume":"08","page":"845-858","_id":"34847","publisher":"World Scientific Pub Co Pte Lt"}]