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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the power series coefficients of certain quotients of Eisenstein series
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by Bruce C. Berndt and Paul R. Bialek PDF
Trans. Amer. Math. Soc. 357 (2005), 4379-4412 Request permission


In their last joint paper, Hardy and Ramanujan examined the coefficients of modular forms with a simple pole in a fundamental region. In particular, they focused on the reciprocal of the Eisenstein series $E_6(\tau )$. In letters written to Hardy from nursing homes, Ramanujan stated without proof several more results of this sort. The purpose of this paper is to prove most of these claims.
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Additional Information
  • Bruce C. Berndt
  • Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
  • MR Author ID: 35610
  • Email:
  • Paul R. Bialek
  • Affiliation: Department of Mathematics, Trinity International University, 2065 Half Day Road, Deerfield, Illinois 60015
  • Email:
  • Received by editor(s): September 30, 2000
  • Received by editor(s) in revised form: June 1, 2003
  • Published electronically: June 9, 2005
  • Additional Notes: The first author’s research was partially supported by grant MDA904-00-1-0015 from the National Security Agency.
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4379-4412
  • MSC (2000): Primary 11F30, 11F27, 33E05
  • DOI:
  • MathSciNet review: 2156715