Higher-genus Fay-like identities from meromorphic generating functions
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...
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2025-03-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.3.093 |
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| author | Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli |
| author_facet | Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli |
| author_sort | Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0bbcf46da83a441d851846171a98cc90 |
| institution | DOAJ |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-0bbcf46da83a441d851846171a98cc902025-08-20T02:52:31ZengSciPostSciPost Physics2542-46532025-03-0118309310.21468/SciPostPhys.18.3.093Higher-genus Fay-like identities from meromorphic generating functionsKonstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis MoeckliA 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.https://scipost.org/SciPostPhys.18.3.093 |
| spellingShingle | Konstantin Baune, Johannes Broedel, Egor Im, Artyom Lisitsyn, Yannis Moeckli Higher-genus Fay-like identities from meromorphic generating functions SciPost Physics |
| title | Higher-genus Fay-like identities from meromorphic generating functions |
| title_full | Higher-genus Fay-like identities from meromorphic generating functions |
| title_fullStr | Higher-genus Fay-like identities from meromorphic generating functions |
| title_full_unstemmed | Higher-genus Fay-like identities from meromorphic generating functions |
| title_short | Higher-genus Fay-like identities from meromorphic generating functions |
| title_sort | higher genus fay like identities from meromorphic generating functions |
| url | https://scipost.org/SciPostPhys.18.3.093 |
| work_keys_str_mv | AT konstantinbaunejohannesbroedelegorimartyomlisitsynyannismoeckli highergenusfaylikeidentitiesfrommeromorphicgeneratingfunctions |