Résume | Multiple zeta values are natural generalizations of thevalues of the zeta function at positive integers. A lot of work wasdone in recent years on relations between these values. The doubleshuffle relations is a linear relation obtained from two productformulas: the series shuffle formula, which follows from an easyseries manipulation, and the integral shuffle formula, which issomewhat more involved.Recently, Furusho defined p-adic multiple zeta values using Colemanintegration. In his theory the integral shuffle formula follows butthe easier series formula was missing.The talk will describe the proof of the series shuffle formula givenin my joint work with Furusho. The new ingredients are the use ofColeman integration in several variables and the use of Deligne'stangential basepoint. |