Fischler, Stephane and Sprang, Johannes and Zudilin, Wadim (2019) Many odd zeta values are irrational. COMPOSITIO MATHEMATICA, 155 (5). pp. 938-952. ISSN 0010-437X, 1570-5846
Full text not available from this repository. (Request a copy)Abstract
Building upon ideas of the second and third authors, we prove that at least 2((1-epsilon)(log s)/(log log s)) values of the Riemann zeta function at odd integers between 3 and s are irrational, where epsilon is any positive real number and s is large enough in terms of epsilon. This lower bound is asymptotically larger than any power of log s; it improves on the bound (1 - epsilon)(log s) / (1 + log 2) that follows from the Ball-Rivoal theorem. The proof is based on construction of several linear forms in odd zeta values with related coefficients.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | NUMBERS ZETA(5); irrationality; zeta values; hypergeometric series |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Guido Kings |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Apr 2020 06:06 |
| Last Modified: | 15 Apr 2020 06:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27067 |
Actions (login required)
 |
View Item |
