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 ...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.展开更多
基金Supported by the National Research and Development Program of China(Grant No.2018YFB1107402)。
文摘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.
