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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Vector-valued Maass-Poincaré series
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by Sharon Anne Garthwaite PDF
Proc. Amer. Math. Soc. 136 (2008), 427-436 Request permission

Abstract:

Shortly before his death, Ramanujan wrote about his discovery of mock theta functions, functions with interesting analytic properties. Recently, Zweger showed that mock theta functions could be “completed” to satisfy the transformation properties of a weight $1/2$ real analytic vector-valued modular form. Using Maass-Poincaré series, Bringmann and Ono proved the Andrews-Dragonette conjecture, establishing an exact formula for the coefficients of Ramanujan’s mock theta function $f(q)$. In this paper we study vector-valued Maass-Poincaré series of all weights, and give their Fourier expansions.
References
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Additional Information
  • Sharon Anne Garthwaite
  • Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
  • Email: sharon.garthwaite@bucknell.edu
  • Received by editor(s): April 16, 2006
  • Received by editor(s) in revised form: October 17, 2006
  • Published electronically: November 1, 2007
  • Additional Notes: This research was supported by the University of Wisconsin at Madison NSF VIGRE program
  • Communicated by: Ken Ono
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 427-436
  • MSC (2000): Primary 11F30; Secondary 11F37
  • DOI: https://doi.org/10.1090/S0002-9939-07-08961-7
  • MathSciNet review: 2358480