Hecke operators for weakly holomorphic modular forms and supersingular congruences

DOI10.1090/S0002-9939-08-09277-0zbMath1173.11028MaRDI QIDQ3522301

Pavel I. Guerzhoy

Publication date: 1 September 2008

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

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Congruences for modular and (p)-adic modular forms (11F33)

Related Items (23)

Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms ⋮ Secord-order cusp forms and mixed mock modular forms ⋮ Linear relations between modular forms for \(\Gamma_0^+(p)\) ⋮ Algebraic de Rham theory for weakly holomorphic modular forms of level one ⋮ ARITHMETIC PROPERTIES OF CERTAIN LEVEL ONE MOCK MODULAR FORMS ⋮ Mock modular period functions and $L$-functions of cusp forms in higher level cases ⋮ Special $L$-values and periods of weakly holomorphic modular forms ⋮ Hecke structures of weakly holomorphic modular forms and their algebraic properties ⋮ Differential operators on Jacobi forms of half integral weight ⋮ Eichler-Shimura theory for mock modular forms ⋮ The \(p\)-adic constant for mock modular forms associated to CM forms ⋮ Half-integral weight \(p\)-adic coupling of weakly holomorphic and holomorphic modular forms ⋮ Weakly holomorphic Hecke eigenforms and Hecke eigenpolynomials ⋮ Regularized inner products and weakly holomorphic Hecke eigenforms ⋮ Congruences for Hecke eigenvalues in higher level cases ⋮ Period functions associated to real-analytic modular forms ⋮ Shintani lifts and fractional derivatives for harmonic weak Maass forms ⋮ Arithmetic of weakly holomorphic Hecke eigenforms ⋮ Periods of Eisenstein series and some applications ⋮ A class of non-holomorphic modular forms. III: real analytic cusp forms for \(\mathrm{SL}_2(\mathbb{Z})\) ⋮ Meromorphic modular forms and the three-loop equal-mass banana integral ⋮ The spaces of new forms for harmonic weak Maass forms and their level raising properties modulo \(\ell\) ⋮ Iterated primitives of meromorphic quasimodular forms for 𝑆𝐿₂(ℤ)

Cites Work

• Dyson's ranks and Maass forms
• Invarianten linearer Differentialgleichungen
• The arithmetic of the values of modular functions and the divisors of modular forms
• Lifting cusp forms to Maass forms with an application to partitions
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