# Phénomènes de symétrie dans des formes linéaires en polyzêtas

Abstract : We give two generalizations, in arbitrary depth, of the symmetry phenomenon used by Ball-Rivoal to prove that infinitely many values of Riemann $\zeta$ function at odd integers are irrational. These generalizations concern multiple series of hypergeometric type, which can be written as linear forms in some specific multiple zeta values. The proof makes use of the regularization procedure for multiple zeta values with logarithmic divergence.
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Preprints, Working Papers, ...

Cited literature [12 references]

https://hal.archives-ouvertes.fr/hal-00101377
Contributor : Jacky Cresson <>
Submitted on : Monday, February 12, 2007 - 12:32:01 PM
Last modification on : Sunday, April 7, 2019 - 3:00:03 PM
Document(s) archivé(s) le : Tuesday, September 21, 2010 - 12:40:07 PM

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### Citation

Jacky Cresson, Stéphane Fischler, Tanguy Rivoal. Phénomènes de symétrie dans des formes linéaires en polyzêtas. 2007. ⟨hal-00101377v2⟩

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