{"date_updated":"2024-05-28T08:28:42Z","status":"public","date_created":"2024-05-28T08:28:13Z","abstract":[{"text":"We answer various questions concerning the distribution of extensions of a\r\ngiven central simple algebra $K$ over a number field. Specifically, we give\r\nasymptotics for the count of inner Galois extensions $L|K$ of fixed degree and\r\ncenter with bounded discriminant. We also relate the distribution of outer\r\nextensions of $K$ to the distribution of field extensions of its center $Z(K)$.\r\nThis paper generalizes the study of asymptotics of field extensions to the\r\nnoncommutative case in an analogous manner to the program initiated by\r\nDeschamps and Legrand to extend inverse Galois theory to skew fields.","lang":"eng"}],"_id":"54482","citation":{"mla":"Gundlach, Fabian, and Béranger Seguin. “Asymptotics of Extensions of Simple $\\mathbb Q$-Algebras.” <i>ArXiv:2405.17286</i>, 2024.","short":"F. Gundlach, B. Seguin, ArXiv:2405.17286 (2024).","ama":"Gundlach F, Seguin B. Asymptotics of extensions of simple $\\mathbb Q$-algebras. <i>arXiv:240517286</i>. Published online 2024.","bibtex":"@article{Gundlach_Seguin_2024, title={Asymptotics of extensions of simple $\\mathbb Q$-algebras}, journal={arXiv:2405.17286}, author={Gundlach, Fabian and Seguin, Béranger}, year={2024} }","apa":"Gundlach, F., &#38; Seguin, B. (2024). Asymptotics of extensions of simple $\\mathbb Q$-algebras. In <i>arXiv:2405.17286</i>.","ieee":"F. Gundlach and B. Seguin, “Asymptotics of extensions of simple $\\mathbb Q$-algebras,” <i>arXiv:2405.17286</i>. 2024.","chicago":"Gundlach, Fabian, and Béranger Seguin. “Asymptotics of Extensions of Simple $\\mathbb Q$-Algebras.” <i>ArXiv:2405.17286</i>, 2024."},"publication":"arXiv:2405.17286","external_id":{"arxiv":["2405.17286"]},"author":[{"first_name":"Fabian","id":"100450","full_name":"Gundlach, Fabian","last_name":"Gundlach"},{"full_name":"Seguin, Béranger","last_name":"Seguin","first_name":"Béranger"}],"language":[{"iso":"eng"}],"type":"preprint","user_id":"100450","year":"2024","title":"Asymptotics of extensions of simple $\\mathbb Q$-algebras"}