S. Cohen

activity

20062024

most citedAn asymptotic formula for the number of irreducible transformation shift registers

12 citations · 38 across the 20 of their papers we have counts for

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21 papers · 1 filter

math.NT2024

Triples and quadruples of consecutive squares or non-squares in a finite field

Stephen D. Cohen

Let $\F$ be the finite field of odd prime power order $q$ , We find explicit expressions for the number of triples $\{\al-1,\al,\al+1 \}$ of consecutive non-zero squares in $\F$ and…

math.NT2022

Primitive element pairs with a prescribed trace in the cubic extension of a finite field

Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1

We prove that for any prime power $q \in / {3, 4, 5}$ , the cubic extension $F_{q^{3}}$ of the finite field $F_{q}$ contains a primitive element $ξ$ such that $ξ+ξ^{-1}…

math.NT2021

Primitive elements with prescribed traces

Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1

Given a prime power $q$ and a positive integer $n$ , let $F_{q^{n}}$ denote the finite field with $q^{n}$ elements. Also let $a, b$ be arbitrary members of the ground field $\…

math.NT2021★ 2 cited

Four consecutive primitive elements in a finite field

Tamiru Jarso, Tim Trudgian

For $q$ an odd prime power, we prove that there are always four consecutive primitive elements in the finite field $F_{q}$ when $q > 2401$ .

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.NT2021

The existence of $F_{q}$ -primitive points on curves using freeness

Stephen D. Cohen, Giorgos Kapetanakis, Lucas Reis

Let $C_{Q}$ be the cyclic group of order $Q$ , $n$ a divisor of $Q$ and $r$ a divisor of $Q / n$ . We introduce the set of $(r, n)$ -free elements of $C_{Q}$ and derive a l…

Triples and quadruples of consecutive squares or non-squares in a finite field

Primitive element pairs with a prescribed trace in the cubic extension of a finite field

Primitive elements with prescribed traces

Four consecutive primitive elements in a finite field

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

The existence of Fq​-primitive points on curves using freeness

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

The existence of $F_{q}$ -primitive points on curves using freeness