Coefficients of half-integral weight modular forms modulo \(\ell^{ j }\)

DOI10.1007/s00208-004-0555-9zbMath1082.11023OpenAlexW1977149682MaRDI QIDQ707440

Scott Ahlgren, Matthew Boylan

Publication date: 9 February 2005

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

Full work available at URL: https://doi.org/10.1007/s00208-004-0555-9

zbMATH Keywords

modular formsFourier coefficientsNewman's conjecture

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Forms of half-integer weight; nonholomorphic modular forms (11F37) Congruences for modular and (p)-adic modular forms (11F33)

Related Items (11)

Congruences involving arithmetic progressions for weakly holomorphic modular forms ⋮ Distribution of powers of the partition function modulo \(\ell ^j\) ⋮ Congruences involving the \(U_{\ell}\) operator for weakly holomorphic modular forms ⋮ Distribution of the coefficients of modular forms and the partition function ⋮ Modular forms of half-integral weight with few non-vanishing coefficients modulo $\ell $ ⋮ Congruences for level $1$ cusp forms of half-integral weight ⋮ Weakly holomorphic modular forms of half-integral weight with nonvanishing constant terms modulo $\ell $ ⋮ On the parity of the number of multiplicative partitions and related problems ⋮ Computing the integer partition function ⋮ The algebraic parts of the central values of quadratic twists of modular \(L\)-functions modulo \(\ell\) ⋮ Modular forms of half-integral weight on \(\Gamma_0 (4)\) with few nonvanishing coefficients modulo \(\ell\)

Cites Work

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• On \(\ell\)-adic representations attached to modular forms
• Arithmetic properties of the partition function
• Distribution of the partition function modulo composite integers \(M\)
• A tameness criterion for Galois representations associated to modular forms (mod \(p\))
• Coefficients of half-integral weight modular forms.
• Distribution of the partition function modulo \(m\)
• Nonvanishing modulo \(l\) of Fourier coefficients of half-integral weight modular forms
• Galois properties of points of finite order of elliptic curves
• On modular forms of half integral weight
• Note on the Parity of the Partition Functions.
• Periodicity Modulo m and Divisibility Properties of the Partition Function
• on l-adic representations attached to modular forms II
• Multiplicative Congruence Properties and Density Problems for p(n)
• Formes modulaires de poids $1$
• Congruence properties for the partition function
• Recurrence Formulae for the Coefficients of Modular Forms and Congruences for the Partition Function and for the Coefficients of $j(\tau)$, $(j(\tau) - 1728)^{\frac{1}{2}}$ and $(j(\tau))^{\frac{1}{3}}$.

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