Special $L$-values and periods of weakly holomorphic modular forms

DOI10.1090/S0002-9939-2014-12092-2zbMath1315.11034OpenAlexW2075435375MaRDI QIDQ3190326

Kathrin Bringmann, Karl-Heinz Fricke, Zachary A. Kent

Publication date: 16 September 2014

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-2014-12092-2

zbMATH Keywords

periodsEichler integralspecial values of \(L\)-functionsmock modular formweakly holomorphic modular formweak Maass form

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Modular and automorphic functions (11F03) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11)

Related Items (11)

Meromorphic quasi-modular forms and their \(L\)-functions ⋮ Eichler-Shimura isomorphism and vector-valued Hecke eigenpolynomials ⋮ Kontsevich-Zagier integrals for automorphic Green's functions. I ⋮ Shintani lifts of nearly holomorphic modular forms ⋮ Analogues of the Bol operator for half-integral weight weakly holomorphic modular forms ⋮ Regularized inner products and weakly holomorphic Hecke eigenforms ⋮ Asymptotic bounds for special values of shifted convolution Dirichlet series ⋮ On cycle integrals of weakly holomorphic modular forms ⋮ Shintani theta lifts of harmonic Maass forms ⋮ Structures for pairs of mock modular forms with the Zagier duality ⋮ Derivatives of \(L\)-series of weakly holomorphic cusp forms

Uses Software

• DLMF

Cites Work

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• Non-vanishing of quadratic twists of modular \(L\)-functions
• On two geometric theta lifts
• Eichler-Shimura theory for mock modular forms
• Nonvanishing theorems for L-functions of modular forms and their derivatives
• p -adic coupling of mock modular forms and shadows
• Hecke operators for weakly holomorphic modular forms and supersingular congruences
• On the order of vanishing of modular $L$-functions at the critical point

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