The transcendence of zeros of natural basis elements for the space of the weakly holomorphic modular forms for Gamma(+)(0)(3)

Abstract

We consider a natural basis for the space of weakly holomorphic modular forms for Gamma(+)(0)(3). We prove that for some of the basis elements, if z(0) in the fundamental domain for Gamma(+)(0)(3) is one of zeroes of the elements, then either z(0) is transcendental or is in {i/root 3,-1+root 2i/3,-3+root 3i/6,-1+root 11i/6}.