An analogue of Ramanujan's sum with respect to regular integers (modr)

被引：6

作者：

Haukkanen, Pentti ^{[1
]}

Toth, Laszlo ^{[2
]}

机构：

[1] Univ Tampere, Dept Math & Stat, Tampere 33014, Finland

[2] Univ Pecs, Inst Math & Informat, H-7624 Pecs, Hungary

来源：

RAMANUJAN JOURNAL | 2012年 / 27卷 / 01期

关键词：

Ramanujan's sum; Regular integer; Arithmetical convolution; Even function; Discrete Fourier transform; Multiplicative function; Mean value; Dirichlet series; SEMI-MULTIPLICATIVE FUNCTIONS;

D O I：

10.1007/s11139-011-9327-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An integer a is said to be regular (modr) if there exists an integer x such that a (2) xa parts per thousand a (mod r). In this paper we introduce an analogue of Ramanujan's sum with respect to regular integers (modr) and show that this analogue possesses properties similar to those of the usual Ramanujan's sum.

引用

页码：71 / 88

页数：18

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