Modular forms of half-integral weight with few non-vanishing coefficients modulo ℓ

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Abstract

Bruinier and Ono classified cusp forms of half-integral weight F(z) := Σn=1 a(n)qn ∈ S λ+1/20(N),χ) ∩ ℤ[[q]] whose Fourier coefficients are not well distributed for modulo odd primes ℓ. Ahlgren and Boylan established bounds for the weight of such a cusp form and used these bounds to prove Newman's conjecture for the partition function for prime-power moduli. In this note, we give a simple proof of Ahlgren and Boylan's result on bounds of cusp forms of half-integral weight.

Original languageEnglish
Pages (from-to)2683-2688
Number of pages6
JournalProceedings of the American Mathematical Society
Volume136
Issue number8
DOIs
Publication statusPublished - 2008 Aug 1
Externally publishedYes

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Keywords

  • Congruences
  • Modular forms

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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