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arXiv:2307.14564 [math.NT]AbstractReferencesReviewsResources

An improved error term for $D_4$-quartic fields

Kevin J. McGown, Amanda Tucker

Published 2023-07-27Version 1

We prove that the number of quartic fields $K$ with discriminant $|\Delta_K|\leq X$ whose Galois closure is $D_4$ equals $CX+O(X^{3/5+\epsilon})$, improving the error term in a well-known result of Cohen, Diaz y Diaz, and Olivier.

Comments: 11 pages, 1 figure
Categories: math.NT
Subjects: 11N45, 11R45, 11R16
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