5 citations · 5 across the 8 of their papers we have counts for
10 papers
The -unit circle
Kenneth Ward
We define the unit circle for global function fields. We demonstrate that this unit circle (endearingly termed the \emph{-unit circle}, after the finite field of…
An explicit triangular integral basis for any separable cubic extension of a function field
Sophie Marques, Kenneth Ward
We determine an explicit triangular integral basis for any separable cubic extension of a rational function field over a finite field in any characteristic. We obtain a formula for…
Cubic Fields: A Primer
Sophie Marques, Kenneth Ward
We classify all cubic extensions of any field of arbitrary characteristic, up to isomorphism, via an explicit construction involving three fundamental types of cubic forms. We dedu…
A complete classification of cubic function fields over any finite field
Sophie Marques, Kenneth Ward
We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain…
Counting roots of truncated hypergeometric series over finite fields
Amit Ghosh, Kenneth Ward
We consider natural polynomial truncations of hypergeometric power series defined over finite fields. For these truncations, we establish asymptotic upper bounds of order $O(p^{11/…
Holomorphic differentials of certain solvable covers of the projective line over a perfect field
Sophie Marques, Kenneth Ward
We provide a Boseck-type basis of the space of holomorphic differentials for a large class of solvable covers of the projective line with perfect field of constants of characterist…
Explicit Galois representations of automorphisms on holomorphic differentials in characteristic
Kenneth Ward
We determine the representation of the group of automorphisms for cyclotomic function fields in characteristic induced by the natural action on the space of holomorphic dif…
Values of twisted Artin -functions
Kenneth Ward
This note gives a simple proof that certain values of Artin's -function, for a representation with character , are stable under twisting by an even Dirichlet character…
The number of roots of polynomials of large degree in a prime field
Amit Ghosh, Kenneth Ward
We establish asymptotic upper bounds on the number of zeros modulo of certain polynomials with integer coefficients, with prime numbers arbitrarily large. The polynomials w…
Asymptotics of class number and genus for abelian extensions of an algebraic function field
Kenneth Ward
Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established. The proof is classical, employing well-known results from…