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Symmetry phenomena in linear forms in multiple zeta values. (Phénomènes de symétrie dans des formes linéaires en polyzêtas.) (English) Zbl 1227.11097
Summary: 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.

11M32 Multiple Dirichlet series and zeta functions and multizeta values
11J72 Irrationality; linear independence over a field
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
Full Text: DOI
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