Some Classical Problems in Number Theory via the Theory of K3 Surfaces

DOI10.1007/978-3-0348-0859-0_10zbMath1333.11038OpenAlexW85480329MaRDI QIDQ3462326

Hironori Shiga

Publication date: 5 January 2016

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0859-0_10

zbMATH Keywords

elliptic curvemodular functionK3 surfacealgebraicityJacobi formula

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (K3) surfaces and Enriques surfaces (14J28) Modular and automorphic functions (11F03)

Cites Work

• Isogeny formulas for the Picard modular form and a three terms arithmetic geometric mean
• Algebraische Punkte auf analytischen Untergruppen algebraischer Gruppen. (Algebraic points on analytic subgroups of algebraic groups)
• On the representation of the Picard modular function by \(\theta\) constants. I-II
• Humbert surfaces and transcendence properties of automorphic functions
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• A variant of Jacobi type formula for Picard curves
• Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines
• ARITHMETIC-GEOMETRIC MEANS FOR HYPERELLIPTIC CURVES AND CALABI–YAU VARIETIES
• Criteria for complex multiplication and transcendence properties of automorphic functions.
• A Cubic Counterpart of Jacobi's Identity and the AGM
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