A variant of Jacobi type formula for Picard curves

DOI10.2969/jmsj/06210305zbMath1188.33022OpenAlexW2007417288MaRDI QIDQ2270229

Hironori Shiga, Keiji Matsumoto

Publication date: 17 March 2010

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/06210305

zbMATH Keywords

theta functionperiod mapAppell's hypergeometric function

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) Appell, Horn and Lauricella functions (33C65)

Related Items (3)

Some Classical Problems in Number Theory via the Theory of K3 Surfaces ⋮ An analogy of Jacobi's formula and its applications ⋮ Cubic modular equations in two variables

Cites Work

• Isogeny formulas for the Picard modular form and a three terms arithmetic geometric mean
• An extended Gauss AGM and corresponding Picard modular forms
• Jacobi's formula for Hesse cubic curves
• On the representation of the Picard modular function by \(\theta\) constants. I-II
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Fonctions hypergeometriques \(F_ 1 \)et fonctions automorphes. I
• A Cubic Counterpart of Jacobi's Identity and the AGM

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