An Elliptic Generalization of Multiple Polylogarithms

Abstract

We introduce a class of functions which constitutes an obvious elliptic generalization of multiple polylogarithms. A subset of these functions appears naturally in the ε-expansion of the imaginary part of the two-loop massive sunrise graph. Building upon the well known properties of multiple polylogarithms, we associate a concept of weight to these functions and show that this weight can be lowered by the action of a suitable differential operator. We then show how properties and relations among these functions can be studied bottom-up starting from lower weights.

27 pages plus three appendices, v2: references added, typos corrected, accepted for publication on NPB

References in corpus (3)

• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
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