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- W2932574490 abstract "In [6], Kohnen proves that if $Gamma=Gamma_0(N)$ where $N$ is a square-free integer, then any modular function of weight $0$ for $Gamma$ having a divisor supported at the cusps is an $eta$-product. Under the condition of having rational Fourier coefficients, we are able to extend Kohnen's result to the case where $N$ is the square of a prime. If the rationality condition does not hold, we show that the statement is no longer true by providing a family of counter-examples that generalizes naturally the Dedekind $eta$-function. This paper fits within the framework of generalized modular forms in the sense of Knopp and Mason." @default.
- W2932574490 created "2019-04-11" @default.
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- W2932574490 date "2016-09-13" @default.
- W2932574490 modified "2023-09-27" @default.
- W2932574490 title "On generalized modular forms with a cuspidal divisor" @default.
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