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arXiv · 1910.09960

Improved lower bounds for the number of fields with alternating Galois group

Aaron Landesman·Robert J. Lemke Oliver·Frank Thorne
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Abstract

Let $n \geq 6$ be an integer. We prove that the number of number fields with Galois group $A_n$ and absolute discriminant at most $X$ is asymptotically at least $X^{1/8 + O(1/n)}$. For $n \geq 8$ this improves upon the previously best known lower bound of $X^{(1 - \frac{2}{n!})/(4n - 4) - \epsilon}$, due to Pierce, Turnage-Butterbaugh, and Wood.

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Aaron Landesman, Robert J. Lemke Oliver, Frank Thorne. 2019-10-22. Improved lower bounds for the number of fields with alternating Galois group. https://doi.org/10.1112/blms.12490

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