Journal of the Ramanujan Mathematical Society

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Mutliple Trigonometry and Zeta Functions


Affiliations
1 Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
2 Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581, Japan
     

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The purpose of this paper is to express the value of the Riemann zeta function at the positive odd integers in terms of the multiple sine functions. We also study the multiple trigonometric functions including the multiple cosine functions. Especially, we derive the algebraic differential equation satisfied by the multiple trigonometric functions.
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  • Mutliple Trigonometry and Zeta Functions

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Authors

Nobushige Kurokawa
Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
Hiroyuki Ochiai
Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan
Masato Wakayama
Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581, Japan

Abstract


The purpose of this paper is to express the value of the Riemann zeta function at the positive odd integers in terms of the multiple sine functions. We also study the multiple trigonometric functions including the multiple cosine functions. Especially, we derive the algebraic differential equation satisfied by the multiple trigonometric functions.