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Explicit Galois representations of automorphisms on holomorphic differentials in characteristic p
  • Kenneth Ward
  • Mathematics, Computer Science
  • Finite Fields Their Appl.
  • 27 August 2014
TLDR
We determine the representation of the Galois group for the cyclotomic function fields in characteristic p 0 induced by the natural action on the space of holomorphic differentials via construction of an explicit canonical basis of differentials. Expand
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Cubic fields: a primer
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 isExpand
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A complete classification of cubic function fields over any finite field
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. InExpand
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Holomorphic differentials of cyclotomic function fields
An explicit triangular integral basis for any separable cubic extension of a function field
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 discriminantExpand
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Holomorphic differentials of solvable Galois towers of curves over a perfect field
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 theExpand
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Counting roots of truncated hypergeometric series over finite fields
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 numberExpand
The Number of Roots of Polynomials of Large Degree in a Prime Field
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
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Asymptotics of class number and genus for abelian extensions of an algebraic function field
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 fieldExpand
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