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arXiv · 2307.14564

An improved error term for counting $D_4$-quartic fields

Kevin J. McGown·Amanda Tucker
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Abstract

We prove that the number of quartic fields $K$ with discriminant $|\Delta_K|\leq X$ whose Galois closure is $D_4$ equals $CX+O(X^{5/8+\varepsilon})$, improving the error term in a well-known result of Cohen, Diaz y Diaz, and Olivier. We prove an analogous result for counting quartic dihedral extensions over an arbitrary base field.

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Kevin J. McGown, Amanda Tucker. 2023-07-27. An improved error term for counting $D_4$-quartic fields. https://arxiv.org/abs/2307.14564

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