Riemann-Wirtinger integrals on the product of two one-dimensional complex tori

Summary · qwen2.5:32b

The article introduces the Riemann-Wirtinger integral extended to the product of two one-dimensional complex tori, generalizing its application beyond a single complex torus. This extension is significant for understanding the structure of associated twisted cohomology groups and deriving related differential equations. The study derives a specific system of differential equations satisfied by this new form of Riemann-Wirtinger integral.

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Excerpt

arXiv:2603.00564v2 Announce Type: replace Abstract: The Riemann-Wirtinger integral is an analogue of the hypergeometric integral defined on a one-dimensional complex torus. As a generalization, we define the Riemann-Wirtinger integral on the product of two one-dimensional complex tori. We study the structure of the twisted cohomology group associated with the Riemann-Wirtinger integral and derive a system of differential equations satisfied by this integral.