Petr Kucheriaviy

activity

20222026

collaborators

4 papers

math.AC2026

An analogue of Rogers' theorem on sieving in commutative rings

Petr Kucheriaviy

We prove that an analogue of Rogers' theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring…

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…

An analogue of Rogers' theorem on sieving in commutative rings

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 $n + w (n)$