Iterated period integrals and multiple Hecke $L$-functions
  In this paper we express the multiple Hecke $L$-function in terms of a linear combination of iterated period integrals associated with elliptic cusp forms, which is introduced by Manin around 2004.   This expression generalizes the classical formula of Hecke $L$-function obtained by the Mellin transformation of a cusp form. Also the expression gives a way of the analytic continuation of the multipleHecke $L$-function. 
YoungJu Choie, Kentaro Ihara
math.NT