论文标题
通过通用矢量扩展，朝椭圆曲线上的代数迭代积分
Towards algebraic iterated integrals on elliptic curves via the universal vectorial extension
论文作者
论文摘要
对于在字段$ k \ subset \ mathbb c $上定义的椭圆曲线$ e $，我们在$ e^\ dagger $上研究对数差分形式的迭代路径积分，这是$ e $的通用矢量扩展。这些是$ e $的经典时期和准期限的概括，并且与多个椭圆形的小聚集体和椭圆形多重Zeta值密切相关。此外，如果$ k $是$ \ mathbb Q $的有限扩展，那么从$ k $ - 理性点之间的路径上的这些迭代积分就在kontsevich-zagier的意义上。
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.
