Hypergeometry inspired by irrationality questions

@article{Krattenthaler2018HypergeometryIB,
title={Hypergeometry inspired by irrationality questions},
author={C. Krattenthaler and W. Zudilin},
journal={arXiv: Number Theory},
year={2018}
}
• Published 2018
• Mathematics
• arXiv: Number Theory
We report new hypergeometric constructions of rational approximations to Catalan's constant, $\log2$, and $\pi^2$, their connection with already known ones, and underlying `permutation group' structures. Our principal arithmetic achievement is a new partial irrationality result for the values of Riemann's zeta function at odd integers.
6 Citations
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Using a new construction of rational linear forms in odd zeta values and the saddle point method, we prove the existence of at least two irrational numbers amongst the 33 odd zeta values ζ(5), ζ(7),.Expand
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Available proofs of result of the type "at least one of the odd zeta values $\zeta(5),\zeta(7),\dots,\zeta(s)$ is irrational" make use of the saddle-point method or of linear independence criteria,Expand

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