Search Results - "Cohen, Stephen D."

FINITE FIELD EXTENSIONS WITH THE LINE OR TRANSLATE PROPERTY FOR -PRIMITIVE ELEMENTS by COHEN, STEPHEN D., KAPETANAKIS, GIORGOS

“…Let $r,n>1$ be integers and $q$ be any prime power $q$ such that $r\mid q^{n}-1$ . We say that the extension $\mathbb{F}_{q^{n}}/\mathbb{F}_{q}$ possesses the…”
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The Making of United States International Economic Policy: Principles, Problems, and Proposals for Reform by Cohen, Stephen D, Volker, Paul

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A proof of the conjecture of Cohen and Mullen on sums of primitive roots by COHEN, STEPHEN D., E SILVA, TOMÁS OLIVEIRA, TRUDGIAN, TIM

“…>. This resolves a conjecture posed by Cohen and Mullen.]]>…”
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Primitive free cubics with specified norm and trace by Huczynska, Sophie, Cohen, Stephen D.

“…The existence of a primitive free (normal) cubic x^3-ax^2+cx-b over a finite field F with arbitrary specified values of a (\neq 0) and b (primitive) is…”
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Polynomial Gauss sums by Cohen, Stephen D., Dewar, Michael, Friedlander, John B., Panario, Daniel, Shparlinski, Igor E.

“…A recent bound for exponential sums by Friedlander, Hansen and Shparlinski is extended to twisted exponential sums with general polynomial arguments. As a…”
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FINITE FIELD EXTENSIONS WITH THE LINE OR TRANSLATE PROPERTY FOR $r$ -PRIMITIVE ELEMENTS by COHEN, STEPHEN D., KAPETANAKIS, GIORGOS

“…Let $r,n>1$ be integers and $q$ be any prime power $q$ such that $r\mid q^{n}-1$ . We say that the extension $\mathbb{F}_{q^{n}}/\mathbb{F}_{q}$ possesses the…”
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Primitive values of rational functions at primitive elements of a finite field by Cohen, Stephen D., Sharma, Hariom, Sharma, Rajendra

“…Given a prime power q and an integer n≥2, we establish a sufficient condition for the existence of a primitive pair (α,f(α)) where α∈Fq and f(x)∈Fq(x) is a…”
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Pairs of primitive elements in fields of even order by Cohen, Stephen D.

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On the least square-free primitive root modulo p by Cohen, Stephen D., Trudgian, Tim

“…Let g□(p) denote the least square-free primitive root modulo p. We show that g□(p)<p0.96 for all p…”
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Primitive elements with prescribed traces by Booker, Andrew R., Cohen, Stephen D., Leong, Nicol, Trudgian, Tim

“…Given a prime power q and a positive integer n, let Fqn denote the finite field with qn elements. Also let a,b be arbitrary members of the ground field Fq. We…”
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The existence of q -primitive points on curves using freeness by Cohen, Stephen D., Kapetanakis, Giorgos, Reis, Lucas

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The existence of $\protect \mathbb{F}_q$-primitive points on curves using freeness by Cohen, Stephen D., Kapetanakis, Giorgos, Reis, Lucas

“…Let $\mathcal{C}_Q$ 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…”
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The orders of related elements of a finite field by COHEN, Stephen D

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An asymptotic formula for the number of irreducible transformation shift registers by Cohen, Stephen D., Hasan, Sartaj Ul, Panario, Daniel, Wang, Qiang

“…We consider the problem of enumerating irreducible transformation shift registers. We give an asymptotic formula for the number of irreducible transformation…”
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The explicit construction of irreducible polynomials over finite fields by Cohen, Stephen D.

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Bivariate factorizations connecting Dickson polynomials and Galois theory by Abhyankar, Shreeram S., Cohen, Stephen D., Zieve, Michael E.

“…In his Ph.D. Thesis of 1897, Dickson introduced certain permutation polynomials whose Galois groups are essentially the dihedral groups. These are now called…”
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Primitive cubics and quartics with zero trace and prescribed norm by Cohen, Stephen D.

“…The proof of the theorem that there exists a primitive polynomial of degree n⩾3 over Fq with arbitrary trace a and arbitrary primitive norm b is completed by…”
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Limits to friendship: Why the United States and the European union have been unable to devise a common trade strategy toward Japan by Cohen, Stephen D.

“…One of the great paradoxes of international economic relations is the ongoing inability of two closely knit allies, the United States and the European Union,…”
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On consecutive primitive elements in a finite field by Cohen, Stephen D., Oliveira e Silva, Tomás, Trudgian, Tim

“…Abstract For $q$ an odd prime power with $q>169,$ we prove that there are always three consecutive primitive elements in the finite field $\mathbb {F}_{q}$…”
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Triples and quadruples of consecutive squares or non-squares in a finite field by Cohen, Stephen D

“…\begin{abstract} 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…”
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