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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.
pdf (270 kb)
tex (8 kb)
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