Number Theory in Function Fields

Table of Contents

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   Book Overview
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   Chapter 1 Polynomials over Finite Fields
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   Chapter 2 Primes, Arithmetic Functions, and the Zeta Function
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   Chapter 3 The Reciprocity Law
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   Chapter 4 Dirichlet L-Series and Primes in an Arithmetic Progression
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   Chapter 5 Algebraic Function Fields and Global Function Fields
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   Chapter 6 Weil Differentials and the Canonical Class
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   Chapter 7 Extensions of Function Fields, Riemann-Hurwitz, and the ABC Theorem
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   Chapter 8 Constant Field Extensions
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    Chapter 9 Galois Extensions — Hecke and Artin L-Series
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    Chapter 10 Artin’s Primitive Root Conjecture
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    Chapter 11 The Behavior of the Class Group in Constant Field Extensions
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    Chapter 12 Cyclotomic Function Fields
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    Chapter 13 Drinfeld Modules: An Introduction
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    Chapter 14 S -Units, S -Class Group, and the Corresponding L-Functions
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    Chapter 15 The Brumer-Stark Conjecture
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    Chapter 16 The Class Number Formulas in Quadratic and Cyclotomic Function Fields
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    Chapter 17 Average Value Theorems in Function Fields