Some applications of modular units

Ick Sun Eum, Ja Kyung Koo, Dong Hwa Shin

Published 2012-07-06, updated 2012-08-05Version 2

We show that a weakly holomorphic modular function can be written as a sum of modular units of higher level. We further find a necessary and sufficient condition for a Siegel modular function of degree $g$ to have neither zero nor pole on the domain when restricted to certain subset of the Siegel upper half-space $\mathbb{H}_g$.