In this work, we study the expansion of a product function U related to the Drinfeld discriminant #DELTA#(z); U is the analogue of the classical #eta#-function. The main result in the formula given in Theorem 3.1. From this formula, we derive the fact that the expansion of U is lacunary for q > 2 (Theorem 3.3) and the expansion (up to a certain bound) of U valid for any q, as in [Gekeler, Invent. Math. 93 (!998), 667-700].
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