Special values of Dirichlet series, monodromy, and the periods of automorphic forms

DOI10.1090/memo/0299zbMath0536.10023OpenAlexW2083695183MaRDI QIDQ3320470

Peter F. Stiller

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1090/memo/0299

zbMATH Keywords

Mellin transformordinary differential equationssubgroups of finite indexDirichlet seriescusp formsspecial linear groupGauss-Manin connectionhypergeometric equationmonodromy representation

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Surfaces and higher-dimensional varieties (14J99)

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A Note on Automorphic Forms of Weight One and Weight Three ⋮ Classical automorphic forms and hypergeometric functions ⋮ A whipple \(_7F_6\) formula revisited ⋮ On the classification of elliptic surfaces with \(q=1\) ⋮ Mixed Jacobi-like forms of several variables ⋮ Level 17 Ramanujan-Sato series ⋮ Differential equations and Hecke operators ⋮ Ramanujan–Sato series for $1/\pi $ ⋮ Apéry limits and special values of \(L\)-functions ⋮ Picard-Fuchs equations for elliptic modular varieties ⋮ Differential equations associated to families of algebraic cycles ⋮ Special values of hypergeometric functions and periods of CM elliptic curves ⋮ Notes on Rankin-Cohen brackets ⋮ A characterization of planar mixed automorphic forms ⋮ Spectral analysis on planar mixed automorphic forms ⋮ Hypergeometric series, modular linear differential equations and vector-valued modular forms ⋮ Periods of mixed automorphic forms and differential equations ⋮ Algebraic hypergeometric transformations of modular origin

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