Cyclotomic p-adic Multi-Zeta Values in Depth Two

Understand

In this paper we compute the values of the p-adic multiple polylogarithms of depth two at roots of unity.

• Our method is to solve the fundamental differential equation satisfied by the crystalline frobenius morphism using rigid analytic methods.
• The main result could be thought of as a computation in the p-adic theory of higher cyclotomy.
• We expect the result to be useful in proving non-vanishing results since it gives quite explicit formulas.