Schwarzian differential equations and Hecke eigenforms on Shimura curves

DOI10.1112/S0010437X12000371zbMath1305.11032arXiv1110.6284MaRDI QIDQ4904423

Yifan Yang

Publication date: 29 January 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.6284

zbMATH Keywords

Shimura curvesHecke operatorsHecke eigenformsSchwarzian differential equations

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 (11)

Ramanujan-type identities for Shimura curves ⋮ Heun functions and diagonals of rational functions ⋮ Quadratic modular symbols on Shimura curves ⋮ Generalized Legendre curves and quaternionic multiplication ⋮ The discriminant 10 Shimura curve and its associated Heun functions ⋮ Automorphic Schwarzian equations ⋮ Special values of hypergeometric functions and periods of CM elliptic curves ⋮ Computing special \(L\)-values of certain modular forms with complex multiplication ⋮ Hypergeometric series, modular linear differential equations and vector-valued modular forms ⋮ Quaternionic modular forms and exceptional sets of hypergeometric functions ⋮ Algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves

Cites Work

• On differential equations satisfied by modular forms
• Construction of class fields and zeta functions of algebraic curves
• Theta series and automorphic forms on \(\text{GL}_2\)
• On the traces of Hecke operators for a normalizer of \(\Gamma_0\)(N)
• Arithmetic $(1;e)$-curves and Belyĭ maps
• Uniformizing functions for certain Shimura curves, in the case D=6

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