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

摘要

Here we prove that Benford's law holds for coefficients of an infinite classof modular forms. Expanding the work of Bringmann and Ono on exact formulas forharmonic Maass forms, we derive the necessary asymptotics. This implies thatthe unrestricted partition function $p(n)$, as well as other natural partitionfunctions, satisfy Benford's law.