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
DOI:
https://doi.org/10.1090/S0002-9939-2010-10577-4
Published electronically:
October 5, 2010
MathSciNet review:
2763743
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
923990
ORCID:
0000-0001-8671-8117
Email:
lrolen@wisc.edu
Ruth Stoehr
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
rstoehr@emory.edu
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.
