Iterated period integrals and multiple Hecke $L$-functions

TL;DR

This paper expresses multiple Hecke L-functions as linear combinations of iterated period integrals of elliptic cusp forms, generalizing classical formulas and providing a method for their analytic continuation.

Contribution

It introduces a novel representation of multiple Hecke L-functions using iterated period integrals, extending classical Mellin transform techniques.

Findings

Provides a new expression for multiple Hecke L-functions

Enables analytic continuation of these functions

Generalizes classical Hecke L-function formula

Abstract

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.