Phénomènes de symétrie dans des formes linéaires en polyzêtas

Details Phénomènes de symétrie dans des formes linéaires en polyzêtas Phénomènes de symétrie dans des formes linéaires en polyzêtas

2006-09-27

arxiv.org/abs/math/0609744v2

Mathematics

Number Theory

45 pages

Scientific paper

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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