V. I. Bernik, N. I. Kalosha, D. V. Vasilyev, “Benford's law and approximation of logarithms of natural numbers by rational numbers”, Proceedings of the Institute of Mathematics of the NAS of Belarus, 2025, Volume 33, Number 1,Pages <nobr>7

ALGEBRA AND NUMBER THEORY

Benford's law and approximation of logarithms of natural numbers by rational numbers

V. I. Bernik, N. I. Kalosha, D. V. Vasilyev

Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk, Belarus

Abstract: The paper is devoted to studying the frequencies at which first digits occur in series formed by powers of integer numbers. A number of generalizations of this problem are considered, and the relation between the distribution of first digits and Diophantine properties of logarithms is discussed. In conclusion of the article, several interesting problems in modern theory of Diophantine approximation are proposed.

Keywords: diophantine approximation, Benford's law, first digit distribution, powers of integers.

UDC: 511.42

Received: 02.04.2025
Revised: 19.05.2025
Accepted: 23.05.2025

Language: English