We classify the cubic rational expressions g(x)/h(x) over a finite field, having at most three ramification points, under an equivalence relation given by preand post-composition with independent Möbius transformations.

In this thesis we consider some problems concerning polynomials over finite fields.
The first topic is the action of some groups on irreducible polynomials. We describe orbits and stabilizers. … Expand

Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of rational functions (up to automorphism of the target) on… Expand

This research focuses on 9 specific elliptic curves E over Q, each with complex multiplication by the maximal order in an imaginary quadratic field, defined by the generators ω1, ω2 ∈ C of the period lattice.Expand

Polynomials over Finite Fields.- Primes, Arithmetic Functions, and the Zeta Function.- The Reciprocity Law.- Dirichlet L-series and Primes in an Arithmetic Progression.- Algebraic Function Fields and… Expand

The one sentence proof is that any number that divides a and b must also divide b and r (since r = a ? qb) and vice versa; hence, the pairs (a, b) and (b, r) have the exact same set of common… Expand