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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2018-08

Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante and Lorenzo Tancredi

 

Elliptic polylogarithms and two-loop Feynman integrals.

 

Abstract: We review certain classes of iterated integrals that appear in the computation of Feynman inte- grals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are closely related to the elliptic multiple polylogarithms (eMPLs) studied in the mathematics literature. When evaluated at certain special values of the arguments, eMPLs reduce to another class of special functions, defined as iterated integrals of Eisenstein series. As a novel application of our formalism, we illustrate how a class of special functions introduced by Remiddi and one of the authors can always naturally be expressed in terms of either eMPLs or iterated integrals of Eisenstein series for the congruence subgroup Γ(6).

 

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2018-08

 

10 pp.