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

 

Benford's law for coefficients of modular forms and partition functions


Authors: Theresa C. Anderson, Larry Rolen and Ruth Stoehr
Journal: Proc. Amer. Math. Soc. 139 (2011), 1533-1541
MSC (2010): Primary 11F12, 11F20, 11P82
Published electronically: October 5, 2010
MathSciNet review: 2763743
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Abstract: Here we prove that Benford's law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessary asymptotics. This implies that the unrestricted partition function $ p(n)$, as well as other natural partition functions, satisfies Benford's law.


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Additional Information

Theresa C. Anderson
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: tcanderson@math.brown.edu

Larry Rolen
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: lrolen@wisc.edu

Ruth Stoehr
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: rstoehr@emory.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10577-4
PII: S 0002-9939(2010)10577-4
Received by editor(s): April 30, 2010
Received by editor(s) in revised form: May 5, 2010
Published electronically: October 5, 2010
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.