Coefficients of half-integral weight modular forms Original Research Article

In this paper, we study the distribution of the coefficients a(n) of half-integral weight modular forms modulo odd integers M. As a consequence, we obtain improvements of indivisibility results for the central critical values of quadratic twists of L-functions associated with integral weight newforms established in Ono and Skinner (Fourier coefficients of half-integral weight modular forms modulo ℓ, Ann. of Math. 147 (1998) 453–470). Moreover, we find a simple criterion for proving cases of Newmanʹs conjecture for the partition function.