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Publications Influence

Explicit Galois representations of automorphisms on holomorphic differentials in characteristic p

- Kenneth Ward
- Mathematics, Computer Science
- Finite Fields Their Appl.
- 27 August 2014

TLDR

6 1- PDF

Cubic fields: a primer

- S. Marques, Kenneth Ward
- Mathematics
- 18 March 2017

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. This classification is… Expand

7 1- PDF

A complete classification of cubic function fields over any finite field

- S. Marques, Kenneth Ward
- Mathematics
- 12 December 2016

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 roots of unity. In… Expand

7- PDF

Holomorphic differentials of cyclotomic function fields

- Kenneth Ward
- Mathematics
- 27 August 2014

An explicit triangular integral basis for any separable cubic extension of a function field

- S. Marques, Kenneth Ward
- Mathematics
- 15 June 2017

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 the discriminant… Expand

3- PDF

Holomorphic differentials of solvable Galois towers of curves over a perfect field

- S. Marques, Kenneth Ward
- Mathematics
- 24 July 2015

We give a basis for the space of holomorphic differentials for a natural class of solvable Galois towers of curves with perfect field of constants of characteristic $p > 0$, which depends upon the… Expand

3

Counting roots of truncated hypergeometric series over finite fields

- Amit Ghosh, Kenneth Ward
- Mathematics
- 25 January 2016

We consider natural polynomial truncations of hypergeometric power series defined over finite fields. For these truncations, we establish asymptotic upper bounds of order $O(p^{11/12})$ on the number… Expand

The Number of Roots of Polynomials of Large Degree in a Prime Field

- Amit B. Ghosh, Kenneth Ward
- Mathematics
- 5 October 2012

We establish asymptotic upper bounds on the number of roots modulo p of some polynomials with rational coefficients, with p an arbitrarily large prime numbers, using a variant of Stepanov's method.… Expand

2- PDF

Asymptotics of class number and genus for abelian extensions of an algebraic function field

- Kenneth Ward
- Mathematics
- 24 February 2011

Abstract Among abelian extensions of a congruence function field, an asymptotic relation of class number and genus is established: namely, for such extensions with class number h, genus g, and field… Expand

1- PDF

Asymptotics of class number and genus for abelian extensions of a congruence function field

- Kenneth Ward
- Mathematics
- 24 February 2011

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