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Higher-genus Fay-like identities from meromorphic generating functions
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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.
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Cited by 2 Pith papers
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Degenerations of flat connections on Riemann surfaces
Enriquez and DHS kernels on genus-h surfaces close under non-separating degeneration to genus h-1 kernels with two punctures whose generators are Bernoulli series in the original Lie algebra elements.
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Higher-genus multiple zeta values
The paper defines higher-genus multiple zeta values, regularizes them via Schottky uniformization, and proves and conjectures new identities among them.
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