Kloosterman Sums with Multiplicative Coefficients

2014/01/18 by Ke Гонг, Gong, Ke, Chaohua Jia +1 · 1 citation
Mathematics · #Analytic Number Theory Research #Finite Group Theory Research #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1401.4556

Abstract

Let f(n) be a multiplicative function satisfying |f(n)|≤ 1, q (≤ N²) be a positive integer and a be an integer with (a, q)=1. In this paper, we shall prove that ∑_\substackn≤ N
(n, q)=1f(n)e(an\over q)≪√(τ(q)\over q)Nloglog(6N)+q^1\over 4+ε\over 2N^{1\over 2}(log(6N))^{1\over 2}+N\over √(loglog(6N)), where n is the multiplicative inverse of n such that nn≡ 1 (\rm mod q), e(x)=exp(2πix), τ(q) is the divisor function.

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