Mean value of the character sums over interval \([1,\frac q8)\)
type: Item
instance of: scholarly article
title: Mean value of the character sums over interval \([1,\frac q8)\)
zbMATH Open document ID: 1196.11115
author: Zhefeng Xu
published in: Taiwanese Journal of Mathematics
publication date: 2009-06-23T00:00:00Z
review text: Let \(k\geq2\) be a fixed integer, and \(q>8\) an odd integer. The author studies the character sum \[ S(\chi)=\sum\limits_{1\leq a<\frac{q}{8}}\chi(a). \] More precisely, he studies the \((2k)\)-th moment of \(S(\chi)\) with \(\chi\) varies over the set of primitive even characters to the modulus \(q\). He proves the following. \[ \sum\limits_{\chi\text{ even and primitive}}|S(\chi)|^{2k}=J(q)q^k\sum\limits_{(n,2q)=1}\frac{a_k(n)}{n^2}+O(q^{k+\varepsilon}), \] where \(J(q)\) is the number of primitive even characters to the modulus \(q\), and the terms \(a_k(n)\) are explicitly given, and are bounded by \(O(n^{\varepsilon})\).
reviewed by: Chunlei Liu
Mathematics Subject Classification ID: 11L40
zbMATH DE Number: 5568279
zbMATH Keywords: character sums
zbMATH Keywords: mean value
zbMATH Keywords: asymptotic formula
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500405277
OpenAlex ID: W4252768931
DOI: 10.11650/TWJM/1500405277
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description: scientific article; zbMATH DE number 5568279