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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Modular forms of half-integral weight with few non-vanishing coefficients modulo $ \ell$


Author: D. Choi
Journal: Proc. Amer. Math. Soc. 136 (2008), 2683-2688
MSC (2000): Primary 11F11, 11F33
Published electronically: March 27, 2008
MathSciNet review: 2399029
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Abstract | References | Similar Articles | Additional Information

Abstract: Bruinier and Ono classified cusp forms of half-integral weight

$\displaystyle F(z):=\sum_{n=0}^{\infty}a(n)q^n\in S_{\lambda+\frac{1}{2}}(\Gamma_0(N),\chi)\cap \mathbb{Z}[[q]]$

whose Fourier coefficients are not well distributed for modulo odd primes $ \ell$. 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.


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Additional Information

D. Choi
Affiliation: School of Mathematics, KIAS, 207-43 Cheongnyangni 2-dong 130-722, Korea
Email: choija@postech.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09195-8
PII: S 0002-9939(08)09195-8
Keywords: Modular forms, congruences
Received by editor(s): January 12, 2007
Received by editor(s) in revised form: April 24, 2007
Published electronically: March 27, 2008
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.