A Pólya--Vinogradov inequality for short character sums

2020/02/07 by Bordignon, Matteo
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2002.02640

Abstract

In this paper we obtain a variation of the Pólya--Vinogradov inequality with the sum restricted to a certain height. Assume χ to be a primitive character modulo q, ε> 0 and N≤ q^1-γ, with 0≤ γ≤ 1/3. We prove that |∑_n=1^N χ(n) |≤ c((1)/(3)-γ+ε)√(q)log q with c=2/π²+o(1) if χ is even and c=1/π+o(1) if χ is odd.

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