Dimitrios Charamaras

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20242026

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math.NT2024

Asymptotic independence of $Ω (n)$ and $Ω (n + 1)$ along logarithmic averages

Dimitrios Charamaras, Florian K. Richter

Let $Ω (n)$ denote the number of prime factors of a positive integer $n$ counted with multiplicities. We show that for any bounded functions $a, b : N \to C$ , $$\f…

math.NT2024

On multiplicative recurrence along linear patterns

Dimitrios Charamaras, Andreas Mountakis, Konstantinos Tsinas

In a recent article, Donoso, Le, Moreira and Sun studied sets of recurrence for actions of the multiplicative semigroup $(N, \times)$ and provided some sufficient conditio…

Asymptotic independence of Ω(n) and Ω(n+1) along logarithmic averages

On multiplicative recurrence along linear patterns

Asymptotic independence of $Ω (n)$ and $Ω (n + 1)$ along logarithmic averages