On the generalized Cochrane sum with Dirichlet characters

被引：0

作者：

Wang, Jiankang ^{[1
]}

Xu, Zhefeng ^{[1
]}

Jia, Minmin ^{[1
]}

机构：

[1] Northwest Univ, Res Ctr Number Theory & Its Applicat, Xian 710127, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 12期

基金：

中国国家自然科学基金;

关键词：

generalized Cochrane sum; Dirichlet character; upper bound; mean value; MEAN-VALUE;

D O I：

10.3934/math.20231542

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：30182 / 30193

页数：12

共 13 条

[1] Apostol T. M., 1976, INTRO ANAL NUMBER TH
[2] Liu H. Y., 2004, Soochow J. Math., V30, P165
[3] A note on the upper bound estimate of high-dimensional Cochrane sums
Liu, Huaning
[J]. JOURNAL OF NUMBER THEORY, 2007, 125 (01) : 7 - 13
[4] Liu HY, 2005, RAMANUJAN J, V9, P373
[5] Upper bound estimate of incomplete Cochrane sum
Ma, Yuankui
Peng, Wen
Zhang, Tianping
[J]. OPEN MATHEMATICS, 2017, 15 : 852 - 858
[6] Rademacher H., 1972, The Carus Mathematical Monographs, V16
[7] On the mean value of general Cochrane sum
Ren, Dongmei
Yi, Yuan
[J]. PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2010, 86 (01) : 1A - 5A
[8] Xie M., 2001, Acta Math. Sin. (Chinese Series), V44, P85
[9] On the order of the high-dimensional Cochrane sum and its mean value
Xu, ZF
Zhang, WP
[J]. JOURNAL OF NUMBER THEORY, 2006, 117 (01) : 131 - 145
[10] Some new sums related to D. H. Lehmer problem
Zhang, Han
Zhang, Wenpeng
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2015, 65 (04) : 915 - 922

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