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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 17. Issue 2


Published on

December, 2022


Pages

77-100


DOI

https://doi.org/10.2478/udt-2022-0013

Article

A Note on the Distributions of (log n)mod 1


Authors

Arno Berger


Abstract

For sequences sufficiently close to (a log n), with an arbitrary real constant a, this note describes the precise asymptotics of the associated empirical distributions modulo one, with respect to the Kantorovich metric as well as a discrepancy-style metric. In particular, the note demonstrates how these asymptotics depend on a in a delicate, discontinuous way. The results strengthen and complement known facts in the literature.


Citation

Berger, A. (2022). A Note on the Distributions of (log n)mod 1. Uniform distribution theory, 17(2), 77-100. https://doi.org/10.2478/udt-2022-0013