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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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A derivation of the Hardy-Ramanujan formula from an arithmetic formula
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by Michael Dewar and M. Ram Murty PDF
Proc. Amer. Math. Soc. 141 (2013), 1903-1911 Request permission

Abstract:

We re-prove the Hardy-Ramanujan asymptotic formula for the partition function without using the circle method. We derive our result from recent work of Bruinier and Ono on harmonic weak Maass forms.
References
  • J. H. Bruinier and K. Ono. Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms. arXiv:1104.1182, Apr. 2011.
  • Jan H. Bruinier, Ken Ono, and Robert C. Rhoades, Differential operators for harmonic weak Maass forms and the vanishing of Hecke eigenvalues, Math. Ann. 342 (2008), no. 3, 673–693. MR 2430995, DOI 10.1007/s00208-008-0252-1
  • J. H. Bruinier, K. Ono, and A. Sutherland. Class polynomials for nonholomorphic modular functions, in preparation.
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  • G. H. Hardy and S. Ramanujan. Asymptotic formulae in combinatory analysis. Proc. London Math. Soc. (2), 17:75–115, 1918.
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  • Atle Selberg, Collected papers. Vol. I, Springer-Verlag, Berlin, 1989. With a foreword by K. Chandrasekharan. MR 1117906
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Additional Information
  • Michael Dewar
  • Affiliation: Department of Mathematics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
  • Email: mdewar@mast.queensu.ca
  • M. Ram Murty
  • Affiliation: Department of Mathematics, Queen’s University, Kingston, Ontario, K7L 3N6, Canada
  • MR Author ID: 128555
  • Email: murty@mast.queensu.ca
  • Received by editor(s): September 22, 2011
  • Published electronically: December 26, 2012
  • Additional Notes: The first author was supported by a postdoctoral fellowship from the Natural Sciences and Engineering Council of Canada (NSERC)
    The second author was supported by a Discovery Grant from NSERC
  • Communicated by: Ken Ono
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 1903-1911
  • MSC (2010): Primary 11E16, 11F03, 11P82
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11458-3
  • MathSciNet review: 3034417