A generalized Ramanujan sum over a residually finite Dedekind domain

被引：0
|
作者：
Qi, T. [1 ]
机构：
[1] Nanjing Inst Technol, Dept Math & Phys, Nanjing 211167, Peoples R China
来源：
ACTA MATHEMATICA HUNGARICA | 2025年
关键词：
Ramanujan sum; arithmetic function; Ramanujan expansion; Dedekind domain; residually finite ring; EXPANSIONS;
D O I：
10.1007/s10474-025-01522-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper extends the Cohen-Ramanujan sum originally defined by Cohen to arbitrary residually finite Dedekind domains. We derive further properties that can be viewed as generalizations of those provided by Zheng [16] and Zheng-Chen-Hong [27]. In particular, we illustrate that the set of the Cohen-Ramanujan sums can be used as a basis for Fourier expansions just as the classical Ramanujan sums can.
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页码：333 / 351
页数：19
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