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Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes
Dohoon Choi
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Recently, Bruinier and Ono classified cusp forms f(z) := ∑ₙ₌₀^∞ a_f(n)q ⁿ ∈S_(λ+1/2)(Γ₀(N),χ)∩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 ≥5. As applications of our main theorem we derive distribution properties, for modulo primes p≥5, of traces of singular moduli and Hurwitz class number. We also study an analogue of Newman's conjecture for overpartitions.
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