1 citations · 1 across the 2 of their papers we have counts for
6 papers
Constructions using Galois Theory
Claus Fieker, Nicole Sutherland
We describe algorithms to compute fixed fields, splitting fields and towers of radical extensions without using polynomial factorisation in towers or constructing any field contain…
The Hasse Norm Principle in Global Function Fields
Adelina Mânzăţeanu, Rachel Newton, Ekin Ozman +2
Let be a finite extension of . We calculate the proportion of polynomials of degree in that are everywhere locally norms from $L/\mathbb{…
Primitive values of quadratic polynomials in a finite field
Andrew R. Booker, Stephen D. Cohen, Nicole Sutherland +1
We prove that for all , there always exists a primitive root in the finite field such that is also a primitive root, where …
Linear combinations of primitive elements of a finite field
Stephen Cohen, Tomás Oliveira e Silva, Nicole Sutherland +1
We examine linear sums of primitive roots and their inverses in finite fields. In particular, we refine a result by Li and Han, and show that every has a pair of primitive…
Galois groups over rational function fields and explicit Hilbert irreducibility
David Krumm, Nicole Sutherland
Let be a polynomial in two variables with rational coefficients, and let be the Galois group of over the field . It follows from Hilbert'…
Existence results for primitive elements in cubic and quartic extensions of a finite field
Geoff Bailey, Stephen D. Cohen, Nicole Sutherland +1
With $\Fq$ the finite field of elements, we investigate the following question. If generates $\Fqn$ over $\Fq$ and is a non-zero element of $\Fqn$, is there always an $…