Sums with convolutions of Dirichlet characters
type: Item
instance of: scholarly article
title: Sums with convolutions of Dirichlet characters
zbMATH Open document ID: 1221.11172
author: William D. Banks
author: Igor E. Shparlinski
published in: Manuscripta Mathematica
publication date: 2010-09-10T00:00:00Z
review text: Let \(\chi_1\) and \(\chi_2\) be primitive Dirichlet characters with conductors \(q_1\) and \(q_2\), respectively, and let \[ S_{\chi_1,\chi_2}(X):=\sum_{ab\leq X}\chi_1(a)\chi_2(b). \] The authors prove that if \(X\geq q_2^{\frac 23}\geq q_1^{\frac 23}\) and \(\log X=q_2^{o(1)}\), then \[ \left| S_{\chi_1,\chi_2}(X)\right|\leq X^{\frac {13}{18}}q_1^{\frac{2}{27}}q_2^{\frac 19+o(1)}. \] If \(X\geq q_2^{\frac 34}\geq q_1^{\frac 34} \) and \(\log X=q_2^{o(1)}\) then \[ \left| S_{\chi_1,\chi_2}(X)\right|\leq X^{\frac {5}{8}}q_1^{\frac{3}{32}}q_2^{\frac {3}{16}+o(1)}. \]
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11L40
zbMATH DE Number: 5782781
zbMATH Keywords: Dirichlet character
zbMATH Keywords: convolution sum
MaRDI profile type: Publication
full work available at URL: s00229-010-0364-2
OpenAlex ID: W1998643756
cites work: Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings, and Fixed Points of the Discrete Logarithm
cites work: Summation Formulae for Coefficients of L-functions
cites work: Q4830109
cites work: On Larcher's theorem concerning good lattice points and multiplicative subgroups modulo p
DOI: 10.1007/S00229-010-0364-2
description: scientific article; zbMATH DE number 5782781