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SIGMA 20 (2024), 060, 11 pages arXiv:1811.10476
https://doi.org/10.3842/SIGMA.2024.060
Some Differential Equations for the Riemann $\theta$-Function on Jacobians
Robert Wilms
Laboratoire de Mathématiques Nicolas Oresme, Université de Caen-Normandie, BP 5186, 14032 Caen Cedex, France
Received March 08, 2024, in final form June 26, 2024; Published online July 02, 2024
Abstract
We prove some differential equations for the Riemann theta function associated to the Jacobian of a Riemann surface. The proof is based on some variants of a formula by Fay for the theta function, which are motivated by their analogues in Arakelov theory of Riemann surfaces.
Key words: $\theta$-functions; Riemann surfaces; Jacobians; differential equations.
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References
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