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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Divisibility properties of coefficients of level $p$ modular functions for genus zero primes
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by Nickolas Andersen and Paul Jenkins
Proc. Amer. Math. Soc. 141 (2013), 41-53
DOI: https://doi.org/10.1090/S0002-9939-2012-11434-0
Published electronically: May 3, 2012
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Abstract:

Lehner’s 1949 results on the $j$-invariant showed high divisibility of the function’s coefficients by the primes $p\in \{2,3,5,7\}$. Expanding his results, we examine a canonical basis for the space of level $p$ modular functions holomorphic at the cusp $0$. We show that the Fourier coefficients of these functions are often highly divisible by these same primes.
References
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Bibliographic Information
  • Nickolas Andersen
  • Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
  • Email: nickolasandersen@gmail.com
  • Paul Jenkins
  • Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
  • Email: jenkins@math.byu.edu
  • Received by editor(s): June 6, 2011
  • Published electronically: May 3, 2012
  • Additional Notes: The first author thanks the Brigham Young University Department of Mathematics for its generous support, as well as Dr. Darrin Doud for his instruction and guidance.
  • Communicated by: Matthew A. Papanikolas
  • © 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), 41-53
  • MSC (2010): Primary 11F03, 11F33
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11434-0
  • MathSciNet review: 2988709