Iterated period integrals and multiple Hecke L-functions

I introduce the multiple Heche L-function associated to elliptic cuspforms and discuss the relations
among special values of the function. Around 2005, Y.I. Manin introduced a generalization of the
period integralof cusp forms by using iterated integral (as an analogy of the iterated integral
expression of the 'multiple zeta values') and studied variousproperties.

In this talk, I show the analytic continuation of the multiple L-functionand give an explicit
description of the Manin's iterated integral in terms ofthe L-functions, which generalizes the
classical formula obtained by Mellin transformation of a cusp form. (This part is a
joint work with Y. Choie).  Secondly, I introduce the graded algebra (say period algebra)
over Qgenerated by the critical values of the L-functions associated to weight two cusp
forms and discuss the number of algebra generators in each grading of the algebra.