On the generalized Cochrane sum with Dirichlet characters

In this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters a...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 12; pp. 30182 - 30193
Main Authors Wang, Jiankang, Xu, Zhefeng, Jia, Minmin
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
dirichlet character
generalized cochrane sum
mean value
upper bound
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Summary:In this paper, we defined a new generalized Cochrane sum with Dirichlet characters, and gave the upper bound of the generalized Cochrane sum with Dirichlet characters. Moreover, we studied the asymptotic estimation problem of the mean value of the generalized Cochrane sum with Dirichlet characters and obtained a sharp asymptotic formula for it. By using this asymptotic formula, we also gave the mean value of the generalized Dedekind sum.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231542