Shifted Character Sums with Multiplicative Coefficients, II

2016/11/20 by Gong, K., Jia, C., Korolev, M. A.
#11L40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1611.06577

Abstract

Let f(n) be a multiplicative function with |f(n)|≤ 1, q be a prime number and a be an integer with (a, q)=1, χ be a non-principal Dirichlet character modulo q. Let ε be a sufficiently small positive constant, A be a large constant, q^\frac12+ε≪ N≪ q^A. In this paper, we shall prove that ∑_{n≤ N}f(n)χ(n+a)≪ N(loglog q)/(log q) and that ∑_{n≤ N}f(n)χ(n+a₁)⋯χ(n+a_t)≪ N(loglog q)/(log q), where t≥ 2, a₁, …, a_t are distinct integers modulo q.

Related

• Shifted Character Sums with Multiplicative Coefficients
• Large values of character sums with multiplicative coefficients
• Large character sums with multiplicative coefficients
• Character sums over shifted primes
• Ω-bounds for the partial sums of some modified Dirichlet characters II