- Title
- Many values of the Riemann zeta function at odd integers are irrational
- Creator
- Fischler, Stéphane; Sprang, Johannes; Zudilin, Wadim
- Relation
- Comptes Rendus Mathematique Vol. 356, Issue 7, p. 707-711
- Publisher Link
- http://dx.doi.org/10.1016/j.crma.2018.05.007
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2018
- Description
- In this note, we announce the following result: at least 2(1-e)[formula could not be replicated] values of the Riemann zeta function at odd integers between 3 and s are irrational, where ε is any positive real number and s is large enough in terms of ε. This improves on the lower bound [formula could not be replicated] log s that follows from the Ball-Rivoal theorem. We give the main ideas of the proof, which is based on an elimination process between several linear forms in odd zeta values with related coefficients.
- Subject
- Riemann zeta function; Ball–Rivoal theorem; integers; mathematics
- Identifier
- http://hdl.handle.net/1959.13/1390132
- Identifier
- uon:33002
- Identifier
- ISSN:1631-073X
- Rights
- © 2018 Académie des sciences. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
- Language
- eng
- Full Text
- Reviewed
- Hits: 1710
- Visitors: 1842
- Downloads: 166
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT02 | Publisher version (open access) | 222 KB | Adobe Acrobat PDF | View Details Download |