Abstract
Bruinier and Ono classified cusp forms of half-integral weight F(z) := Σ∞n=1 a(n)qn ∈ S λ+1/2 (Γ0(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 language | English |
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Pages (from-to) | 2683-2688 |
Number of pages | 6 |
Journal | Proceedings of the American Mathematical Society |
Volume | 136 |
Issue number | 8 |
DOIs | |
Publication status | Published - 2008 Aug |
Externally published | Yes |
Keywords
- Congruences
- Modular forms
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics