F. Thorne

activity

20112025

most citedSecondary terms in counting functions for cubic fields

64 citations · 140 across the 23 of their papers we have counts for

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Showing 2019Show all

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math.NT2019

Upper bounds on polynomials with small Galois group

Robert J. Lemke Oliver, Frank Thorne

When monic integral polynomials of degree $n \geq 2$ are ordered by the maximum of the absolute value of their coefficients, the Hilbert irreducibility theorem implies that asympto…

math.NT2019★ 6 cited

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

Aaron Landesman, Robert J. Lemke Oliver, Frank Thorne

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 $X^{1/8 + O (1/ n)}$ .…