Higher-genus Fay-like identities from meromorphic generating functions
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916655727116288 |
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| author | Baune, Konstantin Broedel, Johannes Im, Egor Lisitsyn, Artyom Moeckli, Yannis |
| author_facet | Baune, Konstantin Broedel, Johannes Im, Egor Lisitsyn, Artyom Moeckli, Yannis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-genus Fay-like identities from meromorphic generating functions Baune, Konstantin Broedel, Johannes Im, Egor Lisitsyn, Artyom Moeckli, Yannis High Energy Physics - Theory Algebraic Geometry 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. |
| title | Higher-genus Fay-like identities from meromorphic generating functions |
| topic | High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2409.08208 |