On the mean values of certain character sums
type: Item
instance of: scholarly article
title: On the mean values of certain character sums
zbMATH Open document ID: 1303.11093
DOI: 10.1155/2013/326597
author: Zhefeng Xu
author: Huaning Liu
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Let \(q\geq 5\) be an odd number, this paper gives asymptotic formulae to the character sums: \[ \mathop{\sum\nolimits^{*}}_{\substack{\chi \mod q,\\ \chi(-1)=-1}}\left|\sum_{1\leq a\leq q/4}a\chi(a)\right|^{4} \] and \[ \mathop{\sum\nolimits^{*}}_{\substack{\chi \mod q,\\ \chi(-1)=1}} \left|\sum_{1\leq a\leq q/4}a\chi(a)\right|^{4}, \] where \(\sum^{*}\) denotes the summation over primitive characters modulo \(q\). The authors express the character sum in terms of Gauss sums and \(L\)-functions, then the mean values of \(L\)-functions give the asymptotic formulae.
reviewed by: Zaizhao Meng
Mathematics Subject Classification ID: 11L05
Mathematics Subject Classification ID: 11L40
zbMATH DE Number: 6306659
zbMATH Keywords: character sum
zbMATH Keywords: primitive character
zbMATH Keywords: fourth power mean
zbMATH Keywords: Gauss sum
Wikidata QID: Q58915951
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/326597
OpenAlex ID: W2000303930
cites work: On Sums Involving Quadratic Characters
cites work: On a question of Ayoub, Chowla and Walum concerning character sums
cites work: A Class of Character Sums
cites work: On certain character sums
cites work: Q4855911
cites work: Q3431304
cites work: Mean values of character sums II
cites work: On the 2kth power mean of the character sums over short intervals
cites work: Fourth power mean of character sums
cites work: Classical theorems on quadratic residues
cites work: On a Cochrane sum and its hybrid mean value formula.
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description: scientific article; zbMATH DE number 6306659