February 26, 2003

Hidekazu Furusho

Title: On p-adic multiple polylogarithms and p-adic multiple zeta values


We introduce (one variable) p-adic multiple polylogarithms by Coleman's p-adic iterated integration theory. We define p-adic multiple zeta values to be special values of p-adic multiple polylogarithms. We show various properties of p-adic multiple zeta values, which are sometimes analogous to the complex case and are sometimes peculiar to the p-adic case. Finally we show that p-adic multiple zeta values come from Besser-Vologodsky's Frobenius invariant path on the p-adic rigid fundamental torsor of the projective line minus three points and discuss on corresponding objects in Galois side and in Hodge side.