Elliptic hyperlogarithms

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 $A_{\mathcal{E}\setminus S}$ of holomorphic multivalued functions on $\mathcal{E}\setminus S$ which is stable under integration, introduced in arXiv:2212.03119; this basis is alternative to the basis of $A_{\mathcal{E}\setminus S}$ constructed in loc. cit. using elliptic analogues of the hyperlogarithm functions.

37 pages; the results have been improved

Cited by in corpus (5)

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