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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.

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Rationality of the Folsom-Ono grid
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by P. Guerzhoy PDF
Proc. Amer. Math. Soc. 137 (2009), 1569-1577 Request permission


In a recent paper Folsom and Ono constructed a grid of Poincaré series of weights $3/2$ and $1/2$. They conjectured that the coefficients of the holomorphic parts of these series are rational integers. We prove that these coefficients are indeed rational numbers with bounded denominators.
  • Basmaji, Jacques, Em Algorithmus zur Berechnung von Hecke-Operatoren Anwendung auf modulare Kurven, Dissertation Essen (1996).
  • 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
  • Kathrin Bringmann and Ken Ono, Arithmetic properties of coefficients of half-integral weight Maass-Poincaré series, Math. Ann. 337 (2007), no. 3, 591–612. MR 2274544, DOI 10.1007/s00208-006-0048-0
  • Jan Hendrik Bruinier and Jens Funke, On two geometric theta lifts, Duke Math. J. 125 (2004), no. 1, 45–90. MR 2097357, DOI 10.1215/S0012-7094-04-12513-8
  • Bruinier, Jan H.; Ono, Ken, Heegner divisors, $L$-functions and harmonic weak Maass forms, preprint.
  • Bruinier, Jan H.; Ono, Ken; Rhoades, Robert C., Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues, Math. Ann. 342 (2008), no. 3, 673–693.
  • H. Cohen and J. Oesterlé, Dimensions des espaces de formes modulaires, Modular functions of one variable, VI (Proc. Second Internat. Conf., Univ. Bonn, Bonn, 1976) Lecture Notes in Math., Vol. 627, Springer, Berlin, 1977, pp. 69–78 (French). MR 0472703
  • Duke, W.; Jenkins, Paul, On the zeros and coefficients of certain weakly holomorphic modular forms, Pure Appl. Math. Q. 4 (2008), no. 4, part 1, 1327–1340.
  • Amanda Folsom and Ken Ono, Duality involving the mock theta function $f(q)$, J. Lond. Math. Soc. (2) 77 (2008), no. 2, 320–334. MR 2400394, DOI 10.1112/jlms/jdm119
  • Sharon Anne Garthwaite, Vector-valued Maass-Poincaré series, Proc. Amer. Math. Soc. 136 (2008), no. 2, 427–436. MR 2358480, DOI 10.1090/S0002-9939-07-08961-7
  • Guerzhoy, P., On weak harmonic Maass-modular grids of even integral weights, Math. Res. Lett., to appear.
  • Ken Ono, The web of modularity: arithmetic of the coefficients of modular forms and $q$-series, CBMS Regional Conference Series in Mathematics, vol. 102, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2004. MR 2020489
  • Ono, Ken, A mock theta function for the Delta-function, Proceedings of the 2007 Integers Conference, accepted for publication.
  • Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, vol. 11, Princeton University Press, Princeton, NJ, 1994. Reprint of the 1971 original; Kanô Memorial Lectures, 1. MR 1291394
  • Don Zagier, Traces of singular moduli, Motives, polylogarithms and Hodge theory, Part I (Irvine, CA, 1998) Int. Press Lect. Ser., vol. 3, Int. Press, Somerville, MA, 2002, pp. 211–244. MR 1977587
  • 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
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Additional Information
  • P. Guerzhoy
  • Affiliation: Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Honolulu, Hawaii 96822-2273
  • Email:
  • Received by editor(s): June 23, 2008
  • Received by editor(s) in revised form: June 28, 2008
  • Published electronically: December 11, 2008
  • Additional Notes: The author was supported by NSF grant DMS-0700933
  • Communicated by: Ken Ono
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1569-1577
  • MSC (2000): Primary 11F37
  • DOI:
  • MathSciNet review: 2470814