Some new identities involving Dedekind sums and the Ramanujan sum

被引：5

作者：

Han, Di ^{[1
]}

Zhang, Wenpeng ^{[1
]}

机构：

[1] NW Univ Xian, Sch Math, Xian 710069, Shaanxi, Peoples R China

来源：

RAMANUJAN JOURNAL | 2014年 / 35卷 / 02期

关键词：

Dedekind sums; Ramanujan sum; Mean value; Dirichlet L-functions;

D O I：

10.1007/s11139-014-9591-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main purpose of this paper is to introduce new sums that are analogous to Dedekind sums. Using analysis and properties of Dirichlet L-functions, we study mean values for these new sums, and give a sharper mean value formula for it.

引用

页码：253 / 262

页数：10

共 10 条

[1] Carlitz L., 1953, PAC J MATH, V3, P513
[2] Mean values of dedekind sums
Conrey, JB
Fransen, E
Klein, R
Scott, C
[J]. JOURNAL OF NUMBER THEORY, 1996, 56 (02) : 214 - 226
[3] Gou S, 2012, B MATH SOC SCI MATH, V55, P209
[4] Ireland K., 1982, CLASSICAL INTRO MODE
[5] On the mean value of Dedekind sums
Jia, CH
[J]. JOURNAL OF NUMBER THEORY, 2001, 87 (02) : 173 - 188
[6] Rademacher H., 1972, DEDEKIND SUMS, P18
[7] Tom M . Apostol., 1976, Introduction to analytic number theory
[8] Tom MA, 1976, MODULAR FUNCTIONS DI
[9] Zhang W. P., 1996, Journal de Theorie des Nombres de Bordeaux, V8, P429, DOI [10.5802/jtnb.179, DOI 10.5802/JTNB.179]
[10] A note on the mean square value of the Dedekind sums
Zhang, WP
[J]. ACTA MATHEMATICA HUNGARICA, 2000, 86 (04) : 275 - 289

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