HYPERGEOMETRIC SERIES AND ARITHMETIC–GEOMETRIC MEAN OVER 2-ADIC FIELDS

DOI10.1142/S1793042112500480zbMath1271.11108MaRDI QIDQ2880341

Kensaku Kinjo, Yuken Miyasaka

Publication date: 13 April 2012

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

zbMATH Keywords

arithmetic-geometric mean\(p\)-adic hypergeometric differential equationunit root of an elliptic curve

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Curves over finite and local fields (11G20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Cites Work

• Variation of the unit root along the Dwork family of Calabi-Yau varieties
• A rigid analytic version of M. Artin's theorem on analytic equations
• Bessel functions as p-adic functions of the argument
• p-adic hypergeometric functions and their cohomology
• Finiteness and cohomological purity in rigid cohomology (with an appendix by Aise Johan de Jong)
• \(p\)-adic cycles
• Formal cohomology. I
• Formal cohomology. II: The cohomology sequence of a pair
• On the solutions of analytic equations
• Formal cohomology. III: Fixed point theorems

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