Journal of the Ramanujan Mathematical Society

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On ζ(3)


Affiliations
1 Department of Mathematics, Tokyo Institute of Technology, Meguro Tokyo, 152-0033, Japan
2 Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, 812-8581, Japan
     

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We prove a certain expression for ζ(3) using a theory of multiple sine functions. This expression has an interesting character indicating a “regulator” part as log S31/2, S3(x) being the triple sine function. The value S3(1/2) is interpreted also as the Mahler measure or the entropy of the associated dynamical system.

Keywords

Riemann Zeta, Triple Sine Function, Multiple Sine Functions, Selberg Zeta.
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  • On ζ(3)

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Authors

Nobushige Kurokawa
Department of Mathematics, Tokyo Institute of Technology, Meguro Tokyo, 152-0033, Japan
Masato Wakayama
Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, 812-8581, Japan

Abstract


We prove a certain expression for ζ(3) using a theory of multiple sine functions. This expression has an interesting character indicating a “regulator” part as log S31/2, S3(x) being the triple sine function. The value S3(1/2) is interpreted also as the Mahler measure or the entropy of the associated dynamical system.

Keywords


Riemann Zeta, Triple Sine Function, Multiple Sine Functions, Selberg Zeta.