IJPAM: Volume 91, No. 1 (2014)

NEGATION OF THE CONJECTURE FOR ODD ZETA VALUES

Takaaki Musha
Advanced Science-Technology Research Organization
3-11-7-601, Namiki, Kanazawa-ku, Yokohama, 236-0005, JAPAN


Abstract. It is known the Euler formula: For even zeta values, $\zeta(2n)=\alpha_n\pi^{2n}$, where $\alpha_n$ is a rational number. It seems natural to conjecture that we can have $\zeta(n)=\alpha_n\pi^n$ for every $n$, but this paper gives the negation of this conjecture for odd zeta values.

Received: December 7, 2013

AMS Subject Classification: 11A25, 11M06, 11Y60, 14G10

Key Words and Phrases: Riemann zeta function, odd zeta values, multiple sine functions

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DOI: 10.12732/ijpam.v91i1.11 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 1