Convolutions on the complex torus

Abstract

``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared recently in the computation of Feynman integrals. The two approaches are related by a sequence of polynomials closely tied to the Eulerian polynomials.

18 pages, to be published in Int. J. Number Theory

References in corpus (2)

• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• The $(2,5)$ minimal model on genus two surfaces

Cited by in corpus (4)

• Numerical evaluation of iterated integrals related to elliptic Feynman integrals
• Modular transformations of elliptic Feynman integrals
• The $(2,5)$ minimal model on genus two surfaces
• A Feynman integral depending on two elliptic curves