Number Theory in Function Fields

Graduate Texts in Mathematics #210

by Michael I. Rosen

* 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 Global Function Fields * Weil Differentials and the Canonical Class * Extensions of Function Fields, Riemann-Hurwitz, and the ABC Theorem * Constant Field Extensions * Galois Extensions - Artin and Hecke L-functions * Artin's Primitive Root Conjecture * The Behavior of the Class Group in Constant Field Extensions * Cyclotomic Function Fields * Drinfeld Modules, An Introduction * S-Units, S-Class Group, and the Corresponding L-functions * The Brumer-Stark Conjecture * Class Number Formulas in Quadratic and Cyclotomic Function Fields * Average Value Theorems in Function Fields

376 pages, Paperback

First published January 8, 2002