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

2010/09/03 by Theresa C. Anderson, Larry Rolen, Anderson, Theresa +3 · 1 citation
Computer Science · Mathematics · #Analytic Number Theory Research #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1009.0780

openalex publication_date 2010/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, satisfy Benford's law.

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• Rectangle partitions generalizing integer partitions

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