Towards algebraic iterated integrals on elliptic curves via the universal vectorial extension

Abstract

For an elliptic curve $E$ defined over a field $k\subset \mathbb{C}$, we study iterated path integrals of logarithmic differential forms on $E^{†}$, the universal vectorial extension of $E$. These are generalizations of the classical periods and quasi-periods of $E$, and are closely related to multiple elliptic polylogarithms and elliptic multiple zeta values. Moreover, if $k$ is a finite extension of $\mathbb{Q}$, then these iterated integrals along paths between $k$-rational points are periods in the sense of Kontsevich--Zagier.

arXiv comment12 pages; for proceedings of workshop "Various aspects of multiple zeta values", RIMS, Kyoto, Japan, 18th-22nd. November. 2019

References in corpus (5)

• Multiple Elliptic Polylogarithms
• Towards multiple elliptic polylogarithms
• Notes on the Universal Elliptic KZB Equation
• On the de Rham and p-adic realizations of the Elliptic Polylogarithm for CM elliptic curves
• The elliptic KZB connection and algebraic de Rham theory for unipotent fundamental groups of elliptic curves

Cited by in corpus (1)

• Meromorphic modular forms and the three-loop equal-mass banana integral