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arXiv · 1911.10634

Long nonnegative sums of Legendre symbols

Alexander Kalmynin
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Abstract

For $0\leq α<1$ and prime number $p$ let $L(α,p)$ be the sum of the first $[αp]$ values of Legendre symbol modulo $p$. We study positivity of $L(α,p)$ and prove that for $|α-\frac13|<2\cdot 10^{-6}$ and for rational $α\leq \frac12$ with denominators in the set $\{1,2,3,4,5,6,8,12\}$ the inequality $L(α,p)\geq 0$ holds for majority of primes.

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Alexander Kalmynin. 2021-06-30. Long nonnegative sums of Legendre symbols. https://arxiv.org/abs/1911.10634

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