Some Differential Equations for the Riemann θ-Function on Jacobians

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2024
• 1. Verfasser: Wilms, Robert
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2024
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/212247
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Some Differential Equations for the Riemann θ-Function on Jacobians. Robert Wilms. SIGMA 20 (2024), 060, 11 pages

We prove some differential equations for the Riemann theta function associated with 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.