Multiple Modular Values and the relative completion of the fundamental group of $M_{1,1}$

Abstract

Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the upper half plane generalising the iterated Shimura integrals of Manin. In this paper, some first properties of the underlying theory are established in the case of the full modular group: in particular, the relationship with special values of L-functions of modular forms at all positive integers; and the action of the conjectural motivic Galois group via a certain group of automorphisms.

Substantially expanded compared with the first version, which is now the first of three parts. The two new parts discuss Hodge-theoretic and Tannakian aspects of the relative completion of the fundamental group of M_{1,1}

References in corpus (2)

• Towards multiple elliptic polylogarithms
• Deligne-Beilinson Cohomology of Affine Groups

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