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- W4300822832 abstract "The Burgess inequality is the best upper bound we have for the character sum $S_{chi}(M,N) = sum_{M<nle M+N} chi(n).$ Until recently, no explicit estimates had been given for the inequality. In 2006, Booker gave an explicit estimate for quadratic characters which he used to calculate the class number of a 32-digit discriminant. McGown used an explicit estimate to show that there are no norm-Euclidean Galois cubic fields with discriminant greater than $10^{140}$. Both of their explicit estimates are on restricted ranges. In this paper we prove an explicit estimate that works for any $M$ and $N$. We also improve McGown's estimates in a slightly narrower range, getting explicit estimates for characters of any order. We apply the estimates to the question of how large must a prime $p$ be to ensure that there is a $k$-th power non-residue less than $p^{1/6}$." @default.
- W4300822832 created "2022-10-04" @default.
- W4300822832 creator A5028025364 @default.
- W4300822832 date "2014-12-09" @default.
- W4300822832 modified "2023-10-16" @default.
- W4300822832 title "The Burgess inequality and the least k-th power non-residue" @default.
- W4300822832 doi "https://doi.org/10.48550/arxiv.1412.3062" @default.
- W4300822832 hasPublicationYear "2014" @default.
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