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arXiv · 2307.01833

Elliptic hyperlogarithms

Benjamin Enriquez·Federico Zerbini
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Abstract

Let $\mathcal E$ be a complex elliptic curve and $S$ be a non-empty finite subset of $\mathcal E$. We show that the functions $\tilde\Gamma$ introduced in arXiv:1712.07089 out of string theory motivations give rise to a basis of the minimal algebra $A_{\mathcal E\smallsetminus S}$ of holomorphic multivalued functions on $\mathcal E\smallsetminus S$ which is stable under integration, introduced in arXiv:2212.03119; this basis is alternative to the basis of $A_{\mathcal E\smallsetminus S}$ constructed in loc. cit. using elliptic analogues of the hyperlogarithm functions.

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Benjamin Enriquez, Federico Zerbini. 2023-07-04. Elliptic hyperlogarithms. https://doi.org/10.4153/s0008414x24001068

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