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Zbl 1241.11102
Musha, Takaaki
On special values of the Riemann zeta function for odd positive integers.
(English)
[J] JP J. Algebra Number Theory Appl. 17, No. 1, 41-49 (2010). ISSN 0972-5555

Summary: This paper presents negation of the conjecture for odd zeta values that there exist positive integers $p_n$ and $q_n$ satisfying $\zeta (2n+1) = (p_n/q_n)\pi^{2n+1}$ for every positive integer $n$. It also presents the numerical calculation result on the Euler's conjecture for the special value of $\zeta (3)$.
MSC 2000:
*11M06 Riemannian zeta-function and Dirichlet L-function
11Y60 Evaluation of constants
14G10 Zeta-functions and related questions

Keywords: Riemann zeta function; special value; Euler's conjecture

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