On Ramanujan Sums over a Dedekind Domain with Finite Norm Property  

作　　者：Zhi Yong ZHENG Man CHEN Zi Wei HONG 

机构地区：[1]School of Mathematics,Renmin University of China,Beijing 100872,P.R.China [2]School of Mathematical Sciences,Beihang University,Beijing 100191,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第1期149-160,共12页数学学报（英文版）

基　　金：Supported by the National Research and Development Program of China(Grant No.2018YFB1107402)。

摘　　要：In this paper,we consider Ramanujan’s sums over arbitrary Dedekind domain with finite norm property.We define the Ramanujan’s sumsη(a,A)andη(B,A),where a is an arbitrary element in a Dedekind domain,B is an ideal and A is a non-zero ideal.In particular,we discuss the Kluyver formula and Hèolder formula forη(a,A)andη(B,A).We also prove the reciprocity formula enjoyed byη(B,A)and the orthogonality relations forη(a,A)in the last two parts.

关 键 词：Dedekind domains Ramanujan Sums primitive additive character reciprocity formula orthogonality property 

分 类 号：O156.4[理学—数学]