Many odd zeta values are irrational

被引：17

作者：

Fischler, Stephane ^{[1
]}

Sprang, Johannes ^{[2
]}

Zudilin, Wadim ^{[3
]}

机构：

[1] Univ Paris Saclay, Lab Math Orsay, Univ Paris Sud, CNRS, F-91405 Orsay, France

[2] Univ Regensburg, Fak Math, D-93053 Regensburg, Germany

[3] Radboud Univ Nijmegen, Dept Math, IMAPP, POB 9010, NL-6500 GL Nijmegen, Netherlands

来源：

COMPOSITIO MATHEMATICA | 2019年 / 155卷 / 05期

关键词：

irrationality; zeta values; hypergeometric series; NUMBERS ZETA(5); HYPERGEOMETRY;

D O I：

10.1112/S0010437X1900722X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：938 / 952

页数：15

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