Long nonnegative sums of Legendre symbols

2019/11/24 by Alexander Kalmynin, Kalmynin, Alexander
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1911.10634

openalex publication_date 2019/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For 0≤ 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⋅ 10^-6 and for rational α≤ \frac12 with denominators in the set \1,2,3,4,5,6,8,12\ the inequality L(α,p)≥ 0 holds for majority of primes.

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