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The rationality of vector valued modular forms associated with the Weil representation

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Abstract.

 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].

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA (e-mail: mcgraw@math.wisc.edu), , , , , , US

    William J. McGraw

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  1. William J. McGraw
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Received: 27 September 2001 / Revised version: 22 July 2002 / Published online: 28 March 2003

Mathematics Subject Classification (1991): 11F30; 11F27

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McGraw, W. The rationality of vector valued modular forms associated with the Weil representation. Math. Ann. 326, 105–122 (2003). https://doi.org/10.1007/s00208-003-0413-1

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  • DOI: https://doi.org/10.1007/s00208-003-0413-1

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