On the problem related with a law of the iterated logarithm
https://doi.org/10.22405/2226-8383-2025-26-5-221-245
Abstract
In paper we consider the problem of finding the number of natural numbers that do not
exceed a given 𝑛, satisfying certain conditions for the function 𝜈(𝑚) – the number of prime
divisors of 𝑚. This work summarizes the result of M. V. Leveque, who considered the values
of the function 𝜈 at consecutive terms of the natural series. In contrast, the present article
examines the behavior of this function at consecutive points of an arithmetic progression. The
solution relies on coprimality and the resulting statistical independence of the prime divisors of neighboring terms in the arithmetic progression.
About the Author
Elina Viktorovna Tishchenko
Lomonosov Moscow State University; RTU MIREA
Russian Federation
Russian Federation
postgraduate student
References
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Review
For citations:
Tishchenko E.V. On the problem related with a law of the iterated logarithm. Chebyshevskii Sbornik. 2025;26(5):221-245. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-5-221-245
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