Foundations of Number Theory: The greatest common divisor of two numbers
Prime numbers and factorization into prime factors
The greatest common divisor of several numbers Number-theoretic functions Congruences
Quadratic residues Pell's equation
Brun's Theorem and Dirichlet's Theorem: Introduction
Some elementary inequalities of prime number theory Brun's theorem on prime pairs Dirichlet's theorem on the prime numbers in an arithmetic progression
Further theorems on congruences
Characters; $L$-series; Dirichlet's proof
Decomposition into Two, Three, and Four Squares: Introduction Farey fractions
Decomposition into two squares Decomposition into four squares
Introduction
Lagrange's theorem
Determination of the number of solutions Decomposition into three squares
Equivalence of quadratic forms
A necessary condition for decomposability into three squares
The necessary condition is sufficient
The Class Number of Binary Quadratic Forms: Introduction Factorable and unfactorable forms Classes of forms
The finiteness of the class number Primary representations by forms
The representation of $h(d)$ in terms of $K(d)$ Gaussian sums
Appendix
Introduction
Kronecker's proof
Schur's proof
Mertens' proof Reduction to fundamental discriminants
The determination of $K(d)$ for fundamental discriminants
Final formulas for the class number Appendix
Exercises: Exercises for part one Exercises for part two Exercises for part three
Index of conventions
Index of definitions
Index
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