Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formula

A. Kokotov; D. Korotkin

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arXiv · math/0405042

Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formula

A. Kokotov·D. Korotkin

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Abstract

Let $w$ be an Abelian differential on compact Riemann surface of genus $g\geq 1$. We obtain an explicit holomorphic factorization formula for $ζ$-regularized determinant of the Laplacian in flat conical metrics with trivial holonomy $|w|^2$, generalizing the classical Ray-Singer result in $g=1$.

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BibTeX RIS

A. Kokotov, D. Korotkin. 2008-07-24. Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formula. https://arxiv.org/abs/math/0405042

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