Affiliation: Universite Claude Bernard, Lyon
Email: kratt@euler.univ-lyon1.fr
Title Of Talk: Hypergeometrics and linear forms of zeta values
URL: http://igd.univ-lyon1.fr/~kratt/artikel/kratriv.html
Abstract: Rivoal has recently proved that there are infinitely many values of the Riemann zeta function at odd integers which are irrational. More results in this direction have been found, among which is Zudilin's, saying that one number among zeta(5), zeta(7), zeta(9), zeta(11) is irrational. All these results depend on an arithmetic study of certain linear forms of zeta values. These linear forms are constructed using certain (very-well-poised) hypergeometric series. Using (variations of) an old identity of Andrews between a single hypergeometric sum and a multiple hypergeometric sum, we are able to prove many of the existing conjectures on the arithmetic of such linear forms of zeta values. Ultimately, this work may lead to an improvement of Zudilin's result. This is joint work with Tanguy Rivoal.
Last update made Thu Nov 11 14:46:37 EST 2004.
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