The distribution of arithmetic functions of general random integers

2019/09/03 by Emmanuel Kowalski, Kowalski, Emmanuel
Mathematics · #11Kxx #11Nxx #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1909.00965

openalex publication_date 2019/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques

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