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An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree (2204.01331v2)
Published 4 Apr 2022 in math.NT
Abstract: We prove an improvement on Schmidt's upper bound on the number of number fields of degree $n$ and absolute discriminant less than X for $6 \leq n \leq 94$. We carry this out by improving and applying a uniform bound on the number of monic integer polynomials, having bounded height and discriminant divisible by a large square, that we proved in a previous work.