Algebraic geometry, the study of solutions to polynomial equations and their geometric properties, finds rich interplay with class field theory—a branch of number theory that classifies abelian ...

We study the dynamics of a polynomial map σ(x) on the algebraic closure of the finite field Fq by defining an induced map on the irreducible polynomials over Fq: σ̂(f) = g f(x) divides g(σ(x)). We ...

We provide a number of results that can be used to derive approximations for the Euler product representation of the zeta function of an arbitrary algebraic function field. Three such approximations ...