Modular Forms: Basics and Beyond

DOI10.1007/978-1-4614-2125-2zbMath1234.11049OpenAlexW2477581760MaRDI QIDQ3102769

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Publication date: 25 November 2011

Published in: Springer Monographs in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-2125-2

zbMATH Keywords

Eisenstein seriesmodular formstheta seriesDirichlet seriesShimura lift

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11) Modular correspondences, etc. (11F32) Discontinuous groups and automorphic forms (11Fxx)

Related Items (13)

Hecke operators on certain subspaces of integral weight modular forms ⋮ Some remarks on the critical values of Rankin-Selberg \(L\)-series ⋮ Existential definability and diophantine stability ⋮ ACTION OF <i>E</i>₂ON HECKE EIGENFORMS ⋮ \(\boldsymbol{U_p}\)-operators and congruences for Shimura images ⋮ Quasimodular forms as solutions of modular differential equations ⋮ Genus character L‐functions of quadratic orders and class numbers ⋮ Rankin-Cohen brackets and identities among eigenforms ⋮ The adjoint map of the Serre derivative and special values of shifted Dirichlet series ⋮ On Fourier-Jacobi expansions of real analytic Eisenstein series of degree 2 ⋮ Eigenfunctions of the Fourier transform with specified zeros ⋮ An average of special values of Dirichlet series of Rankin-Selberg type ⋮ Asymptotic expansions for the coefficients of extremal quasimodular forms and a conjecture of Kaneko and Koike

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