R. Popovych

activity

20102025

collaborators

4 papers

math.NT2025

High order elements in extensions of finite fields given by binomials

Roman Popovych

We construct explicitly in any finite field of the form Fq[x]/(x^m-a) elements with multiplicative order at least 2^{(2m)^(1/2)}

math.NT2022

Elements of high order in finite fields specified by binomials

Victor Bovdi, Adama Diene, Roman Popovych

Let $F_{q}$ be a field with $q$ elements, where $q$ is a power of a prime number $p \geq 5$ . For any integer $m \geq 2$ and $a \in F_{q}^{*}$ such that the polynomial $x^{m} - a$ is irreducible…

math.NT2015

Multiplicative orders of elements in Conway towers of finite fields

Roman Popovych

We give a lower bound on multiplicative orders of some elements in defined by Conway towers of finite fields of characteristic two and also formulate a condition under that these e…

math.NT2010

On a multiplicative order of Gauss periods and related questions

Roman Popovych

We obtain explicit lower bounds on multiplicative order of elements that have more general form than finite field Gauss period. In a partial case of Gauss period this bound improve…