Divisibility properties for weakly holomorphic modular forms with sign vectors

Yichao Zhang

Published 2015-03-03Version 1

In this paper, we prove some divisibility results for the Fourier coeffi?cients of reduced modular forms of sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight is non-positive, which is related to the weight of Borcherds lifts when the weight is zero. By considering Hecke operators for the spaces of weakly holomorphic modular forms with sign vectors, and obtain divisibility results in an "orthogonal" direction on reduced modular forms.