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arXiv · 2603.00577

The Wirtinger-type integral for a genus two curve

Yoshiaki Goto
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Abstract

The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand can be regarded as a multivalued function on an elliptic curve. In this paper, we study an analogue of the Wirtinger integral on a hyperelliptic curve of genus two, introduced by Mizutani and Watanabe. We investigate the associated twisted homology and cohomology groups using the hyperelliptic involution and intersection forms.

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Yoshiaki Goto. 2026-02-28. The Wirtinger-type integral for a genus two curve. https://arxiv.org/abs/2603.00577

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