Dedekind symbols with plus reciprocity laws

JOURNAL OF NUMBER THEORY

卷:128

Article

Fukuhara, Shinji

关键词: dedekind sum;    dedekind symbol;    reciprocity law;   

DOI  :  10.1016/j.jnt.2007.05.007

来源: Elsevier

【 摘 要 】

Dedekind symbols are generalizations of the classical Dedekind sums (symbols), and the symbols are determined uniquely by their reciprocity laws, up to an additive constant. For Dedekind symbols D and F, we can consider two kinds of reciprocity laws: D(p, q) - D(q, -p) = R(p, q) and F(p, q) + F(q, -p) = T(p, q). The first type, which we call minus reciprocity laws, have been studied extensively. On the contrary, the second type, which we call plus reciprocity laws, have not yet been investigated. In this note we study fundamental properties of Dedekind symbols with plus reciprocity law F(p, q) + F(q, -p) = T(p, q). We will see that there is a fundamental difference between Dedekind symbols with minus and plus reciprocity laws. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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