On sign changes of q-exponents of generalized modular functions

Let f be a generalized modular function of weight 0 of level N such that its q-exponents c(n)(n>0) are all real, and div(f) is zero. In this note, we show the equidistribution of signs for c(p)(p prime) by using equidistribution theorems for normalized cuspidal eigenforms of integral weight.