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arXiv · 1909.00965

The distribution of arithmetic functions of general random integers

Emmanuel Kowalski
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Abstract

We consider very general "random integers" and (attempt to) prove that many multiplicative and additive functions of such integers have limiting distributions. These integers include, for instance, the curvatures of Apollonian circle packings, trace of Frobenius elements for elliptic curves, the Ramanujan tau-function, Mersenne numbers, and many others.

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Emmanuel Kowalski. 2019-09-03. The distribution of arithmetic functions of general random integers. https://arxiv.org/abs/1909.00965

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