Irrationalité de valeurs de zêta (d'après Apéry, Rivoal, ...)
Abstract
This survey text deals with irrationality, and linear independence over the rationals, of values at positive odd integers of Riemann zeta function. The first section gives all known proofs (and connections between them) of Apéry's Theorem (1978) : $\zeta(3)$ is irrational. The second section is devoted to a variant of the proof, published by Rivoal and BallRivoal, that infinitely many $\zeta(2n+1)$ are irrational. The end of this text deals with more quantitative statements.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2003
 arXiv:
 arXiv:math/0303066
 Bibcode:
 2003math......3066F
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Classical Analysis and ODEs;
 Mathematics  Combinatorics;
 11J72 (Primary) 11G55;
 11M06;
 33C20;
 41A21 (Secondary)
 EPrint:
 Bourbaki Seminar, November 2002