p-Adic multi-zeta values

Let X be the projective line minus 0,1, and ∞ over . The aim of the following is to give a series representations of the p-adic multi-zeta values in the depth two quotient. The approach is to use the lifting of the frobenius which is not a good choice near 1, but which gives simple formulas away from 1, and to relate the action of frobenius on the de Rham path from 0 to ∞ and on the one from 0 to 1. Also some relations between the p-adic multi-zeta values of depth two are obtained.