The Shimura canonical model for the quaternion algebra of discriminant 6 on the Ihara-Kurihara conic

DOI10.1016/j.jnt.2019.02.019zbMath1444.11129OpenAlexW2928775843WikidataQ128128011 ScholiaQ128128011MaRDI QIDQ2631698

Hironori Shiga

Publication date: 16 May 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2019.02.019

zbMATH Keywords

hypergeometric functionsShimura curvescomplex multiplicationPicard modular formsfalse elliptic curvesQM type abelian surfaces

Mathematics Subject Classification ID

Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Classical hypergeometric functions, ({}_2F_1) (33C05)

Cites Work

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• To the Hilbert class field from the hypergeometric modular function
• A new interpretation of the Shimura curve with discriminant 6 in terms of Picard modular forms
• On the representation of the Picard modular function by \(\theta\) constants. I-II
• Arithmétique des algèbres de quaternions
• Arithmetic triangle groups
• Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two
• On equations defining fake elliptic curves
• Construction of class fields and zeta functions of algebraic curves
• Criteria for complex multiplication and transcendence properties of automorphic functions.

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