G. Kapetanakis

activity

20172021

collaborators

7 papers

math.NT2021

The trace of primitive and $2$ -primitive elements in finite fields, revisited

Stephen D. Cohen, Giorgos Kapetanakis

By definition primitive and $2$ -primitive elements of a finite field extension $F_{q^{n}}$ have order $q^{n} - 1$ and $(q^{n} - 1) /2$ , respectively. We have already shown that, with…

math.NT2019

The translate and line properties for 2-primitive elements in quadratic extensions

Stephen D. Cohen, Giorgos Kapetanakis

Let $r, n > 1$ be integers and $q$ be any prime power $q$ such that $r ∣ q^{n} - 1$ . We say that the extension $F_{q^{n}} / F_{q}$ possesses the line property for $r$ -primit…

math.NT2019

Finite field extensions with the line or translate property for $r$ -primitive elements

Stephen D. Cohen, Giorgos Kapetanakis

Let $r, n > 1$ be integers and $q$ be any prime power $q$ such that $r ∣ q^{n} - 1$ . We say that the extension $F_{q^{n}} / F_{q}$ possesses the line property for $r$ -primit…

math.NT2019

The trace of 2-primitive elements of finite fields (amended version)

Stephen D. Cohen, Giorgos Kapetanakis

Let $q$ be a prime power and $n, r$ integers such that $r ∣ q^{n} - 1$ . An element of $F_{q^{n}}$ of multiplicative order $(q^{n} - 1) / r$ is called \emph{ $r$ -primitive}. For any o…

math.NT2018

A Swan-like note for a family of binary pentanomials

Giorgos Kapetanakis

In this note, we employ the techniques of Swan (Pacific J. Math. 12(3): 1099-1106, 1962) with the purpose of studying the parity of the number of the irreducible factors of the pen…

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…

The trace of primitive and 2-primitive elements in finite fields, revisited

The translate and line properties for 2-primitive elements in quadratic extensions

Finite field extensions with the line or translate property for r-primitive elements

The trace of 2-primitive elements of finite fields (amended version)

A Swan-like note for a family of binary pentanomials

Further results on the Morgan-Mullen conjecture

The trace of primitive and $2$ -primitive elements in finite fields, revisited

Finite field extensions with the line or translate property for $r$ -primitive elements