Shifted Character Sums with Multiplicative Coefficients

2014/04/08 by Ke Гонг, Gong, Ke, Chaohua Jia +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1404.2204

openalex publication_date 2014/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(n) be a multiplicative function satisfying |f(n)|≤ 1, q (≤ N²) be a prime number and a be an integer with (a, q)=1, χ be a non-principal Dirichlet character modulo q. In this paper, we shall prove that ∑_{n≤ N}f(n)χ(n+a)≪ N\over q^{1\over 4}loglog(6N)+q^{1\over 4}N^{1\over 2}log(6N)+N\over √(loglog(6N)). We shall also prove that amp;∑_{n≤ N}f(n)χ(n+a₁)⋯χ(n+a_t)≪ N\over q^{1\over 4}loglog(6N)
amp; +q^{1\over 4}N^{1\over 2}log(6N)+N\over √(loglog(6N)), where t≥ 2, a₁, ⋯, a_t are pairwise distinct integers modulo q.

Citations

• Kloosterman Sums with Multiplicative Coefficients

Related

• Shifted Character Sums with Multiplicative Coefficients, II
• Large values of character sums with multiplicative coefficients
• Character sums over shifted primes
• Large character sums with multiplicative coefficients
• Kloosterman Sums with Multiplicative Coefficients