To the Hilbert class field from the hypergeometric modular function

DOI10.1016/j.jnt.2016.01.016zbMath1401.11107arXiv1511.02941OpenAlexW2159198477MaRDI QIDQ271788

Atsuhira Nagano, Hironori Shiga

Publication date: 20 April 2016

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

Full work available at URL: https://arxiv.org/abs/1511.02941

zbMATH Keywords

hypergeometric functionstheta functionscomplex multiplication\(K3\) surfacesHilbert modular formsHilbert class fieldmoduli of abelian varietiesabelian surfacesperiod domains

Mathematics Subject Classification ID

Period matrices, variation of Hodge structure; degenerations (32G20) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Theta functions and abelian varieties (14K25) Theta series; Weil representation; theta correspondences (11F27) Complex multiplication and moduli of abelian varieties (11G15) Deformations of complex structures (32G05)

Related Items

Icosahedral invariants and a construction of class fields via periods of \(K3\) surfaces ⋮ The Shimura canonical model for the quaternion algebra of discriminant 6 on the Ihara-Kurihara conic ⋮ Icosahedral invariants and Shimura curves ⋮ Geometric interpretation of Hermitian modular forms via Burkhardt invariants ⋮ Inverse period mappings of \(K3\) surfaces and a construction of modular forms for a lattice with the Kneser conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A theta expression of the Hilbert modular functions for \(\sqrt{5}\) via the periods of \(K3\) surfaces
• Lattice polarized \(K3\) surfaces and Siegel modular forms
• \(K3\) surfaces with non-symplectic automorphisms of prime order. With an appendix by Shigeyuki Kondō
• Hilbertsche Modulformen und Modulfunktionen zu \({\mathbb{Q}}(\sqrt{5})\) (Hilbert modular forms and modular functions for \({\mathbb{Q}}(\sqrt{5})\))
• Fonctions hypergéométriques \(F_ 1\) et fonctions automorphes. II: Groupes discontinus arithmétiquement définis
• Nikulin involutions on \(K3\) surfaces
• The determination of the imaginary abelian number fields with class number one
• Arithmetic triangle groups
• On the family of pentagonal curves of genus 6 and associated modular forms on the ball.
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• On K3 surfaces with large Picard number
• Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two
• Icosahedral invariants and Shimura curves
• Construction of class fields and zeta functions of algebraic curves
• On compact analytic surfaces. II
• Arithmetic variety of moduli for genus two
• On the Ring of Modular Forms of Degree Two Over Z
• INVOLUTIONS OF INTEGRAL QUADRATIC FORMS AND THEIR APPLICATIONS TO REAL ALGEBRAIC GEOMETRY
• Calculation of the Class Numbers of Imaginary Cyclic Quartic Fields
• Criteria for complex multiplication and transcendence properties of automorphic functions.
• PERIOD DIFFERENTIAL EQUATIONS FOR THE FAMILIES OF K3 SURFACES WITH TWO PARAMETERS DERIVED FROM THE REFLEXIVE POLYTOPES
• On Siegel Modular Forms of Genus Two
• Modular Forms and Projective Invariants
• Algorithmic Number Theory