Half-integral weight \(p\)-adic coupling of weakly holomorphic and holomorphic modular forms

DOI10.1007/s40993-015-0027-1zbMath1380.11043OpenAlexW2254039245MaRDI QIDQ906266

Ben Kane, Kathrin Bringmann, Pavel I. Guerzhoy

Publication date: 21 January 2016

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40993-015-0027-1

zbMATH Keywords

\(p\)-adic congruenceshalf-integral weightShintani liftShimura liftHecke eigenformsweakly holomorphic modular forms

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) (p)-adic theory, local fields (11F85)

Related Items (5)

Explicit construction of mock modular forms from weakly holomorphic Hecke eigenforms ⋮ MAGNETIC (QUASI-)MODULAR FORMS ⋮ \(p\)-adic properties of coefficients of certain half-integral weight modular forms ⋮ On 𝑝-adic harmonic Maass functions ⋮ Shintani lifts and fractional derivatives for harmonic weak Maass forms

Cites Work

• Unnamed Item
• Cycle integrals of the \(j\)-function and mock modular forms
• Modular forms of half-integral weight on \(\Gamma_0(4)\)
• Integral traces of singular values of weak Maass forms
• Values of L-series of modular forms at the center of the critical strip
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• Construction of some families of 2-dimensional crystalline representations
• Eichler-Shimura theory for mock modular forms
• Shintani lifts and fractional derivatives for harmonic weak Maass forms
• Formulas for the coefficients of half-integral weight harmonic Maaß forms
• The vanishing of Ramanujan's function \(\tau(n)\)
• p -adic coupling of mock modular forms and shadows
• Hecke operators for weakly holomorphic modular forms and supersingular congruences
• Mock modular forms as $p$-adic modular forms

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