Petr Kucheriaviy

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20222026

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math.NT2025

Positivity of partial sums of a random multiplicative function and corresponding problems for the Legendre symbol

Petr Kucheriaviy

Let $f (n)$ be a random completely multiplicative function such that $f (p) = \pm 1$ with probabilities $1/2$ independently at each prime. We study the conditional probability, given…

math.NT2024

Erdős inequality for primitive sets

Petr Kucheriaviy

A set of natural numbers $A$ is called primitive if no element of $A$ divides any other. Let $Ω (n)$ be the number of prime divisors of $n$ counted with multiplicity. Let $f_z(A) =…

math.NT2022

On numbers not representable as $n + w (n)$

Petr Kucheriaviy

Let $w (n)$ be an additive non-negative integer-valued arithmetic function which is equal to $1$ on primes. We study the distribution of $n + w (n)$ $(mod p)$ and give a lower bound…

Positivity of partial sums of a random multiplicative function and corresponding problems for the Legendre symbol

Erdős inequality for primitive sets

On numbers not representable as n+w(n)

On numbers not representable as $n + w (n)$