The rationality of vector valued modular forms associated with the Weil representation
- 192 Downloads
In a recent paper [Duke Math. J., 97, 219–233], Borcherds asks whether or not the spaces of vector valued modular forms associated to the Weil representation have bases of modular forms whose Fourier expansions have only integer coefficients. We give an affirmative answer to Borcherds' question. This strengthens and simplifies Borcherds' main theorem which is a generalization of a theorem of Gross, Kohnen, and Zagier [Math. Ann., 278, 497–562].
KeywordsFourier Modular Form Duke Math Fourier Expansion Affirmative Answer
Unable to display preview. Download preview PDF.