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An alternative transformation formula for the Dedekind $η$ -function via the Chinese Remainder Theorem

Department of Mathematics, Faculty of Science, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore

E-mail Address: matchh@nus.edu.sg

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and

Teoh Guan Chua

Department of Mathematics, Faculty of Science, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore

E-mail Address: A0086683@u.nus.edu

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https://doi.org/10.1142/S1793042116500329Cited by:4 (Source: Crossref)

Abstract

In this article, we will give a new proof of the reciprocity law for Dedekind sums, as well as a proof of the transformation formula for the Dedekind $η$ -function using the Chinese Remainder Theorem.

Dedicated to Professor T. M. Apostol

Keywords:

AMSC: 11F20

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