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

Fonseca, T
Matthes, N

## Journal:

RIMS Kokyuroku, no. 2160 (2020), 114--125

## Last Updated:

2020-11-08T00:38:45.06+00:00

## abstract:

For an elliptic curve $E$ defined over a field $k\subset \mathbb C$, we study
iterated path integrals of logarithmic differential forms on $E^\dagger$, 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.

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