Number Theory in Function Fields (Paperback)

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