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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Divisibility properties of coefficients of level $ p$ modular functions for genus zero primes


Authors: Nickolas Andersen and Paul Jenkins
Journal: Proc. Amer. Math. Soc. 141 (2013), 41-53
MSC (2010): Primary 11F03, 11F33
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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11434-0
PII: S 0002-9939(2012)11434-0
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.