Cyclotomic p-adic multi-zeta values

Abstract

The cyclotomic p-adic multi-zeta values are the p-adic periods of pi(uni)(1)(G(m) \ mu M,(.)), the unipotent fundamental group of the multiplicative group minus the M-th roots of unity. In this paper, we compute the cyclotomic p-adic multi-zeta values at all depths. This paper generalizes the results in [9] and [10]. Since the main result gives quite explicit formulas we expect it to be useful in proving non-vanishing and transcendence results for these p-adic periods and also, through the use of p-adic Hodge theory, in proving non-triviality results for the corresponding p-adic Galois representations.