The double shuffle relation for p-adic multiple zeta values
(Un exposé d'Amnon Besser au séminaire de
théorie des nombres de Chevaleret le 2 mai 2005)
Résumé :
Multiple zeta values are natural generalizations of the
values of the zeta function at positive integers. A lot of work was
done in recent years on relations between these values. The double
shuffle relations is a linear relation obtained from two product
formulas: the series shuffle formula, which follows from an easy
series manipulation, and the integral shuffle formula, which is
somewhat more involved.
Recently, Furusho defined p-adic multiple zeta values using Coleman
integration. In his theory the integral shuffle formula follows but
the easier series formula was missing.
The talk will describe the proof of the series shuffle formula given
in my joint work with Furusho. The new ingredients are the use of
Coleman integration in several variables and the use of Deligne's
tangential basepoint.