Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 101, 5 pages      arXiv:1510.01901      https://doi.org/10.3842/SIGMA.2015.101
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications

Hankel Determinants of Zeta Values

Alan Haynes ^a and Wadim Zudilin ^b
a) Department of Mathematics, University of York, York, YO10 5DD, UK
^b) School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan NSW 2308, Australia

Received October 19, 2015, in final form December 16, 2015; Published online December 17, 2015

Abstract
We study the asymptotics of Hankel determinants constructed using the values $\zeta(an+b)$ of the Riemann zeta function at positive integers in an arithmetic progression. Our principal result is a Diophantine application of the asymptotics.

Key words: irrationality; Hankel determinant; zeta value.

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