Benford's Law For Coefficients of Modular Forms and Partition Functions

Details Benford's Law For Coefficients of Modular Forms and Partition Functions Benford's Law For Coefficients of Modular Forms and Partition Functions

2010-09-03

arxiv.org/abs/1009.0780v1

Mathematics

Number Theory

10 pages

Scientific paper

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, satisfy Benford's law.

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