Vol. 2, No. 5, 2008

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Integral traces of singular values of weak Maass forms

William Duke and Paul Jenkins

Vol. 2 (2008), No. 5, 573–593
Abstract

We define traces associated to a weakly holomorphic modular form f of arbitrary negative even integral weight and show that these traces appear as coefficients of certain weakly holomorphic forms of half-integral weight. If the coefficients of f are integral, then these traces are integral as well. We obtain a negative weight analogue of the classical Shintani lift and give an application to a generalization of the Shimura lift.

Keywords
weak Maass forms, weakly holomorphic modular forms, traces of singular moduli
Mathematical Subject Classification 2000
Primary: 11F30
Secondary: 11F37
Milestones
Received: 3 December 2007
Revised: 15 May 2008
Accepted: 13 June 2008
Published: 4 July 2008
Authors
William Duke
UCLA Mathematics Department
Box 951555
Los Angeles, CA 90095-1555
United States
http://www.math.ucla.edu/~wdduke/
Paul Jenkins
UCLA Mathematics Department
Box 951555
Los Angeles, CA 90095-1555
United States
http://www.math.ucla.edu/~jenkins/