Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

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

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Vector-valued Maass-Poincaré series
HTML articles powered by AMS MathViewer

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


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.
  • George E. Andrews, Richard Askey, and Ranjan Roy, Special functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, Cambridge, 1999. MR 1688958, DOI 10.1017/CBO9781107325937
  • Kathrin Bringmann and Ken Ono, Arithmetic properties of coefficients of half-integral weight Maass-Poincaré series, Mathematische Annalen, 337 (2007). 591–612.
  • —, Dyson’s ranks and Maass forms, accepted for publication in Annals of Mathematics.
  • Kathrin Bringmann and Ken Ono, The $f(q)$ mock theta function conjecture and partition ranks, Invent. Math. 165 (2006), no. 2, 243–266. MR 2231957, DOI 10.1007/s00222-005-0493-5
  • Jan H. Bruinier, Borcherds products on O(2, $l$) and Chern classes of Heegner divisors, Lecture Notes in Mathematics, vol. 1780, Springer-Verlag, Berlin, 2002. MR 1903920, DOI 10.1007/b83278
  • Freeman J. Dyson, A walk through Ramanujan’s garden, Ramanujan revisited (Urbana-Champaign, Ill., 1987) Academic Press, Boston, MA, 1988, pp. 7–28. MR 938957
  • Sharon Anne Garthwaite, The coefficients of the $\omega (q)$ mock theta function, Accepted for publication, International Journal of Number Theory.
  • Dennis A. Hejhal, The Selberg trace formula for $\textrm {PSL}(2,\,\textbf {R})$. Vol. 2, Lecture Notes in Mathematics, vol. 1001, Springer-Verlag, Berlin, 1983. MR 711197, DOI 10.1007/BFb0061302
  • Srinivasa Ramanujan, The lost notebook and other unpublished papers, Springer-Verlag, Berlin; Narosa Publishing House, New Delhi, 1988. With an introduction by George E. Andrews. MR 947735
  • S. P. Zwegers, Mock $\theta$-functions and real analytic modular forms, $q$-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000) Contemp. Math., vol. 291, Amer. Math. Soc., Providence, RI, 2001, pp. 269–277. MR 1874536, DOI 10.1090/conm/291/04907
  • Sander Zwegers, Mock theta functions, Ph.D. thesis, Universiteit Utrecht, 2002.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F30, 11F37
  • Retrieve articles in all journals with MSC (2000): 11F30, 11F37
Additional Information
  • Sharon Anne Garthwaite
  • Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
  • Email:
  • 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:
  • MathSciNet review: 2358480