On a hybrid mean value of the character sums over short intervals
type: Item
instance of: scholarly article
title: On a hybrid mean value of the character sums over short intervals
zbMATH Open document ID: 1252.11062
author: Zhefeng Xu
author: Wenpeng Zhang
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2010-01-07T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.facm/1261157804
review text: Let \(B(\chi)\) be the constant in the zero expansion of logarithmic differentiation of the \(L(s,\chi)\), \(S(q/4,\chi)\) be the character sum over \([1,q/4)\). In this paper,the following result is obtained. Theorem. Let \(q\geq 5\), then \[ \sideset\and {^*}\to\sum\limits_{\chi \bmod q} |B(\chi)S(q/4,\chi)|^{2}=CqJ(q)+O(q^{1+\varepsilon}), \] where \(J(q)\) is the number of all primitive characters modulo \(q\). The proofs use the mean value theorems of the \(L\)-functions.
reviewed by: Zaizhao Meng
Mathematics Subject Classification ID: 11L40
zbMATH DE Number: 5654313
zbMATH Keywords: character sums
zbMATH Keywords: hybrid mean value
zbMATH Keywords: asymptotic formula
MaRDI profile type: Publication
OpenAlex ID: W1975462189
cites work: Mean values of character sums II
cites work: On the 2kth power mean of the character sums over short intervals
cites work: Q3900124
cites work: Q4101884
cites work: On a Cochrane sum and its hybrid mean value formula. II
DOI: 10.7169/FACM/1261157804
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description: scientific article; zbMATH DE number 5654313