Formulas for the coefficients of half-integral weight harmonic Maaß forms

DOI10.1007/s00209-014-1278-6zbMath1350.11059arXiv1209.5197OpenAlexW2067531226MaRDI QIDQ2509921

Claudia Alfes-Neumann

Publication date: 31 July 2014

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.5197

zbMATH Keywords

singular moduliharmonic Maass forms

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Fourier coefficients of automorphic forms (11F30)

Related Items (15)

A classification of harmonic weak Maaß forms of half-integral weight ⋮ Weierstrass mock modular forms and elliptic curves ⋮ Singular moduli and the distribution of partition ranks modulo 2 ⋮ Algebraic and transcendental formulas for the smallest parts function ⋮ Half-integral weight \(p\)-adic coupling of weakly holomorphic and holomorphic modular forms ⋮ Effective bounds for traces of weak Maass forms ⋮ On a theta lift related to the Shintani lift ⋮ Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms ⋮ On 𝑝-adic harmonic Maass functions ⋮ Shintani lifts and fractional derivatives for harmonic weak Maass forms ⋮ Class invariants for certain non-holomorphic modular functions ⋮ Integral traces of weak Maass forms of genus zero odd prime level ⋮ Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products ⋮ Bounds for coefficients of the \(f(q)\) mock theta function and applications to partition ranks ⋮ Maass forms and the mock theta function \(f(q)\)

Cites Work

• Heegner divisors, \(L\)-functions and harmonic weak Maass forms
• Explicit formulas for the Fourier coefficients of Jacobi and elliptic modular forms
• Arithmetic properties of coefficients of half-integral weight Maass-Poincaré series
• Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues
• Integral traces of singular values of weak Maass forms
• Twisted traces of singular values
• The theta correspondence and harmonic forms. I
• Heegner points and derivatives of \(L\)-series. II
• Non-vanishing of quadratic twists of modular \(L\)-functions
• Heegner points, cycles and Maass forms
• Borcherds products on \(O(2,l)\) and Chern classes of Heegner divisors
• Errata to: ``CM values of regularized theta lifts and harmonic weak Maaß forms of weight 1
• On two geometric theta lifts
• Twisted traces of CM values of weak Maass forms
• Integrality properties of the CM-values of certain weak Maass forms
• Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
• Nonvanishing of quadratic twists of modular L-functions and applications to elliptic curves
• ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS
• Traces of CM values of modular functions
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