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Higher-genus Fay-like identities from meromorphic generating functions
by Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli
Submission summary
| Authors (as registered SciPost users): | Konstantin Baune |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2409.08208v1 (pdf) |
| Date submitted: | 2024-10-11 17:05 |
| Submitted by: | Baune, Konstantin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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 between 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
In refereeing