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

Anderson, Theresa; Rolen, Larry; Stoehr, Ruth

doi:10.1090/S0002-9939-2010-10577-4

Benford’s law for coefficients of modular forms and partition functions
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by Theresa C. Anderson, Larry Rolen and Ruth Stoehr PDF

Proc. Amer. Math. Soc. 139 (2011), 1533-1541 Request permission

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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