Arithmetic of linear forms involving odd zeta values

Wadim Zudilin

Arithmetic of linear forms involving odd zeta values

Number Theory 2007-05-23 v2 Classical Analysis and ODEs

Authors: Wadim Zudilin

Abstract

A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of $\zeta(2)$ and $\zeta(3)$ , as well as to explain Rivoal's "infinitely-many" result (math.NT/0008051) and to prove that at least one of the four numbers $\zeta(5)$ , $\zeta(7)$ , $\zeta(9)$ , and $\zeta(11)$ is irrational.

Keywords

zeta values and euler sums zeta functions multiple zeta values

Cite

@article{arxiv.math/0206176,
  title  = {Arithmetic of linear forms involving odd zeta values},
  author = {Wadim Zudilin},
  journal= {arXiv preprint arXiv:math/0206176},
  year   = {2007}
}

Comments

42 pages, LaTeX; slight modification of the absract

Arithmetic of linear forms involving odd zeta values

Abstract

Keywords

Cite

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