The main result of this note is a characterization of those generalized modular functions of weight zero on $\Gamma_0(N)$ that have empty divisor, in terms of the growth of the exponents in their $q$-product expansion.
@article{1285679143,
author = {Kohnen, Winfried},
title = {On certain generalized modular forms},
journal = {Funct. Approx. Comment. Math.},
volume = {42},
number = {1},
year = {2010},
pages = { 23-29},
language = {en},
url = {http://dml.mathdoc.fr/item/1285679143}
}
Kohnen, Winfried. On certain generalized modular forms. Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, pp. 23-29. http://gdmltest.u-ga.fr/item/1285679143/