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

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.