Benford’s law and approximation of logarithms of natural numbers by rational numbers
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.
Supporting agencies: This work was supported by the Institute of Mathematics of the National Academy of Sciences of Belarus within the framework of the state programme “Convergence–2020
About the Authors
V. I. Bernik
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
N. I. Kalosha
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Minsk
D. V. Vasilyev
Institute of Mathematics of the National Academy of Sciences of Belarus
Russian Federation
Russian Federation
Minsk
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Review
For citations:
Bernik V.I., Kalosha N.I., Vasilyev D.V. 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;33(1):7-14.
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