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SOME HYPERGEOMETRIC INTEGRALS FOR LINEAR FORMS IN ZETA VALUES

Part of: Diophantine approximation, transcendental number theory Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  19 July 2018

WADIM ZUDILIN Open the ORCID record for WADIM ZUDILIN [Opens in a new window]
WADIM ZUDILIN*
Affiliation:
Department of Mathematics, IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, Netherlands email w.zudilin@math.ru.nl
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Abstract

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We prove new integral representations of the approximation forms in zeta values.

Keywords

Hurwitz zeta functionhypergeometric integralsintegral representation

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$
Secondary: 11J72: Irrationality; linear independence over a field 33C20: Generalized hypergeometric series, $_pF_q$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 372 - 375
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2018 Australian Mathematical Publishing Association Inc.

References

Fischler, S., Sprang, J. and Zudilin, W., ‘Many odd zeta values are irrational’, Preprint, 2018, arXiv:1803.08905 [math.NT]; abridged version, Comptes Rendus Math. Acad. Sci. Paris 356 (2018), 707–711.Google Scholar
Zudilin, W., ‘One of the odd zeta values from 𝜁(5) to 𝜁(25) is irrational. By elementary means’, SIGMA 14 (2018), Article ID 028, 8 pages.Google Scholar