Phénomènes de symétrie dans des formes linéaires en polyzêtas

Jacky Cresson (1) , Stephane Fischler (2) , Tanguy Rivoal (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 IF - Institut Fourier

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.

Domaines: Théorie des nombres [math.NT]

Jacky Cresson, Stephane Fischler, Tanguy Rivoal. Phénomènes de symétrie dans des formes linéaires en polyzêtas. 2006. ⟨hal-00101377v1⟩