Abstract

Speaker: Michel Waldschmidt (Universite de Paris VI)

Title: Multiple zeta values

Abstract:

The values of Riemann's zeta function at positive integers had been studied already by Euler. In his investigation of products of such values he introduced multiple zeta values, namely

sum_{n_1 > n_2 > ... > n_k} n_1^{-s_1}\cdots n_k^{-s_k}

when s_1, ..., s_k are positive integers with n_1 >= 2. These numbers are related by a number of algebraic relations which give rise to a rich algebraic structure. The main open problem is to prove that all such relations are the known ones.

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