This article is cited in 4 papers

Irrationality of the sums of zeta values

T. G. Hessami Pilehrood, Kh. Hessami Pilehrood

Shahrekord University

Abstract: In this paper, we establish a lower bound for the dimension of the vector spaces spanned over $\mathbb Q$ by 1 and the sums of the values of the Riemann zeta function at even and odd points. As a consequence, we obtain numerical results on the irrationality and linear independence of the sums of zeta values at even and odd points from a given interval of the positive integers.

UDC: 511.3

Received: 13.04.2005

DOI: 10.4213/mzm2731

 English version: Mathematical Notes, 2006, 79:4, 561–571

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