The distribution of arithmetic functions of general random integers
Number Theory
2019-09-10 v2 Probability
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.
Keywords
Cite
@article{arxiv.1909.00965,
title = {The distribution of arithmetic functions of general random integers},
author = {Emmanuel Kowalski},
journal= {arXiv preprint arXiv:1909.00965},
year = {2019}
}
Comments
Fatal error in the proof of Th. 1.7; much stronger assumptions are required to obtain limiting distributions