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

## Author:

Jardim Da Fonseca, T
Matthes, N

## Journal:

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

## Last Updated:

2021-01-15T13:14:15.53+00:00

114-125

## abstract:

For an elliptic curve E defined over a field k ⊂ 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 Q, then these iterated integrals along paths between k-rational points are periods in the sense of Kontsevich–Zagier.

1136737

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Conference Paper