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Mathematische Annalen

, Volume 326, Issue 1, pp 105–122 | Cite as

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

  • William J. McGraw

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].

Keywords

Fourier Modular Form Duke Math Fourier Expansion Affirmative Answer 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

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

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