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.
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St Petersburg State Univ, Dept Math & Comp Sci, St Petersburg 199034, RussiaSt Petersburg State Univ, Dept Math & Comp Sci, St Petersburg 199034, Russia
Mortenson, Eric T.
Zwegers, Sander
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Univ Cologne, Dept Math & Comp Sci, Weyertal 86-90, D-50931 Cologne, GermanySt Petersburg State Univ, Dept Math & Comp Sci, St Petersburg 199034, Russia