# Distribution of integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes - Mathematics Number Theory

Abstract: Recently, Bruinier and Ono classified cusp forms $fz := \sum {n=0}^{\infty}a fnq ^n \in S {\lambda+1-2}\Gamma 0N,\chi\cap \mathbb{Z}q$ that doesnot satisfy a certain distribution property for modulo odd primes $p$. In thispaper, using Rankin-Cohen Bracket, we extend this result to modular forms ofhalf integral weight for primes $p \geq 5$. As applications of our main theoremwe derive distribution properties, for modulo primes $p\geq5$, of traces ofsingular moduli and Hurwitz class number. We also study an analogue of Newmansconjecture for overpartitions.

Author: Dohoon Choi

Source: https://arxiv.org/