Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves

DOI10.1090/S0002-9947-2013-05960-0zbMath1355.11032arXiv1112.1001MaRDI QIDQ2855945

Yifan Yang, Fang-Ting Tu

Publication date: 23 October 2013

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

Full work available at URL: https://arxiv.org/abs/1112.1001

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Automorphic forms, one variable (11F12) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (6)

Heun functions and diagonals of rational functions ⋮ Generalized Legendre curves and quaternionic multiplication ⋮ Belyi functions for hyperbolic hypergeometric-to-Heun transformations ⋮ Special values of hypergeometric functions and periods of CM elliptic curves ⋮ Computing special \(L\)-values of certain modular forms with complex multiplication ⋮ Hypergeometric functions over finite fields

Cites Work

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• Schwarzian differential equations associated to Shimura curves of genus zero
• Arithmétique des algèbres de quaternions
• Arithmetic triangle groups
• Transformations of some Gauss hypergeometric functions
• Construction of class fields and zeta functions of algebraic curves
• Uniformizing functions for certain Shimura curves, in the case D=6
• Schwarzian differential equations and Hecke eigenforms on Shimura curves
• Algorithmic Number Theory

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