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 be a random completely multiplicative function such that with probabilities independently at each prime. We study the conditional probability, given…
math.NT2024
Erdős inequality for primitive sets
Petr Kucheriaviy
A set of natural numbers is called primitive if no element of divides any other. Let be the number of prime divisors of counted with multiplicity. Let $f_z(A) =…
math.NT2022
On numbers not representable as
Petr Kucheriaviy
Let be an additive non-negative integer-valued arithmetic function which is equal to on primes. We study the distribution of and give a lower bound…