Benford’s law for coefficients of modular forms and partition functions
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- by Theresa C. Anderson, Larry Rolen and Ruth Stoehr
- Proc. Amer. Math. Soc. 139 (2011), 1533-1541
- DOI: https://doi.org/10.1090/S0002-9939-2010-10577-4
- Published electronically: October 5, 2010
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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.References
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Bibliographic 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2763743