Number Theory in Function Fields

Front Matter....Pages i-xii
Polynomials over Finite Fields....Pages 1-9
Primes, Arithmetic Functions, and the Zeta Function....Pages 11-21
The Reciprocity Law....Pages 23-31
Dirichlet L-Series and Primes in an Arithmetic Progression....Pages 33-43
Algebraic Function Fields and Global Function Fields....Pages 45-61
Weil Differentials and the Canonical Class....Pages 63-76
Extensions of Function Fields, Riemann-Hurwitz, and the ABC Theorem....Pages 77-99
Constant Field Extensions....Pages 101-113
Galois Extensions — Hecke and Artin L-Series....Pages 115-147
Artin’s Primitive Root Conjecture....Pages 149-167
The Behavior of the Class Group in Constant Field Extensions....Pages 169-191
Cyclotomic Function Fields....Pages 193-217
Drinfeld Modules: An Introduction....Pages 219-239
 S -Units, S -Class Group, and the Corresponding L-Functions....Pages 241-256
The Brumer-Stark Conjecture....Pages 257-281
The Class Number Formulas in Quadratic and Cyclotomic Function Fields....Pages 283-303
Average Value Theorems in Function Fields....Pages 305-327
Back Matter....Pages 329-361