One of the Odd Zeta Values from ζ(5) to ζ(25) Is Irrational. By Elementary Means

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Author: Zudilin W.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209436
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: One of the Odd Zeta Values from ζ(5) to ζ(25) Is Irrational. By Elementary Means / W. Zudilin // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 10 назв. — англ.

Available proofs of the result of the type "at least one of the odd zeta values ζ(5), ζ(7),…, ζ(s) is irrational" make use of the saddle-point method or of linear independence criteria, or both. These two remarkable techniques are, however, counted as highly non-elementary, therefore leavi...