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

SIGMA 11 (2015), 101, 5 pages      arXiv:1510.01901
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

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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