T. Garefalakis

activity

20162025

most citedTranslates of completely normal elements and the Morgan-Mullen conjecture

1 citations · 1 across the 3 of their papers we have counts for

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math.NT2025★ 1 cited

Translates of completely normal elements and the Morgan-Mullen conjecture

Theodoulos Garefalakis, Giorgos Kapetanakis

Denote by $F_{q}$ the finite field of order $q$ and by $F_{q^{n}}$ its extension of degree $n$ . Some $a \in F_{q^{n}}$ is called primitive if it generates the multi…

math.NT2018

Further results on the Morgan-Mullen conjecture

Theodoulos Garefalakis, Giorgos Kapetanakis

Let $F_{q}$ be the finite field of characteristic $p$ with $q$ elements and $F_{q^{n}}$ its extension of degree $n$ . The conjecture of Morgan and Mullen asserts the e…

math.NT2017

On the existence of primitive completely normal bases of finite fields

Theodoulos Garefalakis, Giorgos Kapetanakis

Let $F_{q}$ be the finite field of characteristic $p$ with $q$ elements and $F_{q^{n}}$ its extension of degree $n$ . We prove that there exists a primitive element of…

math.NT2016

On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$

Fabio E. Brochero Martínez, Theodoulos Garefalakis, Lucas Reis +1

In this paper, we find a lower bound for the order of the group $⟨ θ + α ⟩ \subset F_{q}^{*}$ , where $α \in F_{q}$ , $θ$ is a generic root of the po…

Translates of completely normal elements and the Morgan-Mullen conjecture

Further results on the Morgan-Mullen conjecture

On the existence of primitive completely normal bases of finite fields

On the multiplicative order of the roots of bXqr+1−aXqr+dX−c

On the multiplicative order of the roots of $b X^{q^{r} + 1} - a X^{q^{r}} + d X - c$