Abstract
We prove several multiplicity one theorems for generalized modular functions (GMF), in terms of their $q$-exponents, and make a precise statement about the nature of values that the prime $q$-exponents of a GMF can take. We shall also study the integrality of general $q$-exponents of a GMF and give an upper bound on the first sign change of these $q$-exponents.
Citation
Narasimha Kumar. "Remarks on $q$-exponents of generalized modular functions." Funct. Approx. Comment. Math. 53 (2) 177 - 188, December 2015. https://doi.org/10.7169/facm/2015.53.2.1
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