This article is cited in 37 papers

Irrationality of values of the Riemann zeta function

W. V. Zudilin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper deals with a generalization of Rivoal's construction, which enables one to construct linear approximating forms in 1 and the values of the zeta function $\zeta(s)$ only at odd points. We prove theorems on the irrationality of the number $\zeta(s)$ for some odd integers $s$ in a given segment of the set of positive integers. Using certain refined arithmetical estimates, we strengthen Rivoal's original results on the linear independence of the $\zeta(s)$.

UDC: 511.3

MSC: 11J81, 11M06

Received: 24.04.2001

DOI: 10.4213/im387

 English version: Izvestiya: Mathematics, 2002, 66:3, 489–542

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