Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes

Details Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes

2007-03-31

arxiv.org/abs/0704.0012v1

Mathematics

Number Theory

Scientific paper

Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty} a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N),\chi)\cap \mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen Bracket, we extend this result to modular forms of half integral weight for primes $p \geq 5$. As applications of our main theorem we derive distribution properties, for modulo primes $p\geq5$, of traces of singular moduli and Hurwitz class number. We also study an analogue of Newman's conjecture for overpartitions.

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