# On the canonical decomposition of generalized modular functions

@inproceedings{Kohnen2010OnTC,
title={On the canonical decomposition of generalized modular functions},
author={Winfried Kohnen and Geoffrey Mason},
year={2010}
}
• Published 11 March 2010
• Mathematics
The authors have conjectured (\cite{KoM}) that if a normalized generalized modular function (GMF) $f$, defined on a congruence subgroup $\Gamma$, has integral Fourier coefficients, then $f$ is classical in the sense that some power $f^m$ is a modular function on $\Gamma$. A strengthened form of this conjecture was proved (loc cit) in case the divisor of $f$ is \emph{empty}. In the present paper we study the canonical decomposition of a normalized parabolic GMF $f = f_1f_0$ into a product of…
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