One of the odd zeta values from \(\zeta(5)\) to \(\zeta(25)\) is irrational. By elementary means

DOI10.3842/SIGMA.2018.028zbMath1445.11063arXiv1801.09895OpenAlexW2786762203MaRDI QIDQ1747886

Wadim Zudilin

Publication date: 27 April 2018

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.09895

zbMATH Keywords

hypergeometric seriesrational functionirrationalityzeta value

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Generalized hypergeometric series, ({}_pF_q) (33C20) Irrationality; linear independence over a field (11J72)

Related Items (7)

SOME HYPERGEOMETRIC INTEGRALS FOR LINEAR FORMS IN ZETA VALUES ⋮ Many odd zeta values are irrational ⋮ A note on the number of irrational odd zeta values ⋮ Irrationality of values of L‐functions of Dirichlet characters ⋮ Many values of the Riemann zeta function at odd integers are irrational ⋮ Arithmetic of Catalan's constant and its relatives ⋮ HYPERGEOMETRY INSPIRED BY IRRATIONALITY QUESTIONS

Cites Work

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• Arithmetic of linear forms involving odd zeta values
• Many values of the Riemann zeta function at odd integers are irrational
• A note on odd zeta values
• Irrationalité d'au moins un des neuf nombres ζ(5), ζ(7),...,ζ(21)
• HYPERGEOMETRY INSPIRED BY IRRATIONALITY QUESTIONS
• On the Product of the Primes
• Irrationality of infinitely many values of the zeta function at odd integers.

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