Large values of character sums with multiplicative coefficients

2025/08/13 by Dong, Zikang, Li, Zhonghua, Song, Yutong +1
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.09750

Abstract

In this article, we investigate large values of Dirichlet character sums with multiplicative coefficients ∑_{n≤ N}f(n)χ(n). We prove an Omega result in the region exp((log q)^\frac12+ε)≤ N≤√ q, where q is the prime modulus.

Citations

• Extreme values of Dirichlet polynomials with multiplicative coefficients
• The maximum size of short character sums

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• Large values of Dirichlet polynomials with multiplicative coefficients
• Shifted Character Sums with Multiplicative Coefficients, II
• Quadratic character sums with multiplicative coefficients
• Large quadratic character sums