Work

Higher-genus Fay-like identities from meromorphic generating functions

Year: 2025

Type: article

Abstract: A possible way of constructing polylogarithms on Riemann surfaces of higher genera facilitates integration kernels, which can be derived from generating functions incorporating the geometry of the surface. Functional relations among polylogarithms rely on identities for those integration kernels. In this article, we derive identities for Enriquez’ meromorphic generating function and investigate the implications for the associated integration kernels. The resulting identities are shown to be exhaustive and therefore reproduce all identities for Enriquez’ kernels conjectured in arXiv:2407.11476 recently.

Source: SciPost Physics

DOI: 10.21468/scipostphys.18.3.093

Authors: Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli

Institution: ETH Zurich

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, National Centres of Competence in Research SwissMAP, Deutsche Forschungsgemeinschaft, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Awards: G1897041155, G4066435496, EXC 2094: ORIGINS: Vom Ursprung des Universums bis zu den ersten Bausteinen des Lebens