Asymptotics of extensions of simple $\mathbb Q$-algebras

F. Gundlach, B. Seguin, ArXiv:2405.17286 (2024).

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Gundlach, FabianLibreCat; Seguin, Béranger
Abstract
We answer various questions concerning the distribution of extensions of a given central simple algebra $K$ over a number field. Specifically, we give asymptotics for the count of inner Galois extensions $L|K$ of fixed degree and center with bounded discriminant. We also relate the distribution of outer extensions of $K$ to the distribution of field extensions of its center $Z(K)$. This paper generalizes the study of asymptotics of field extensions to the noncommutative case in an analogous manner to the program initiated by Deschamps and Legrand to extend inverse Galois theory to skew fields.
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arXiv:2405.17286
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Gundlach F, Seguin B. Asymptotics of extensions of simple $\mathbb Q$-algebras. arXiv:240517286. Published online 2024.
Gundlach, F., & Seguin, B. (2024). Asymptotics of extensions of simple $\mathbb Q$-algebras. In arXiv:2405.17286.
@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} }
Gundlach, Fabian, and Béranger Seguin. “Asymptotics of Extensions of Simple $\mathbb Q$-Algebras.” ArXiv:2405.17286, 2024.
F. Gundlach and B. Seguin, “Asymptotics of extensions of simple $\mathbb Q$-algebras,” arXiv:2405.17286. 2024.
Gundlach, Fabian, and Béranger Seguin. “Asymptotics of Extensions of Simple $\mathbb Q$-Algebras.” ArXiv:2405.17286, 2024.

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