Introduction to Analytic Number Theory

Title page
Chapter I: The unique factorization theorem
1. Primes
2. The unique factorization theorem
3. A second proof of Theorem 2
4. Greatest common divisor and least common multiple
5. Farey sequences
6. The infinitude of primes
Chapter II: Congruences
1. Residue classes
2. Theorems of Euler and of Fermat
3. The number of solutions of a congruence
Chapter III: Rational approximation of irrationals and Hurwitz's theorem
1. Approximation of irrationals
2. Sums of two squares
3. Primes of the form 4k+-1
4. Hurwitz's theorem
Chapter IV: Quadratic residues and the representation of a number as a sum of four squares
1. The Legendre symbol
2. Wilson's theorem and Euler's criterion
3. Sums of two squares
4. Sums of four squares
Chapter V: The law of quadratic reciprocity
1. Quadratic reciprocity
2. Reciprocity for generalized Gaussian sums
3. Proof of quadratic reciprocity
4. Some applications
Chapter VI: Arithmetical functions and lattice points
1. Generalities
2. The lattice point function r(n)
3. The divisor function d(n)
4. The function σ(n)
5. The Möbius function μ(n)
6. Euler's function φ(n)
Chapter VII: Chebyshev's theorem on the distribution of prime numbers
1. The Chebyshev functions
2. Chebyshev's theorem
3. Bertrand's postulate
4. Euler's identity
5. Some formulae of Mertens
Chapter VIII: Weyl's theorems on uniform distribution and Kronecker's theorem
1. Introduction
Z. Uniform distribution in the unit interval
3. Uniform distribution modulo 1
4. Weyl's theorems
5. Kronecker's theorem
Chapter IX: Minkowski's theorem on lattice points in convex sets
1. Convex sets
2. Minkowski's theorem
3. Applications
Chapter X: Dirichlet's theorem on primes in an arithmetical progression
1. Introduction
2. Characters
3. Sums of characters, orthogonality relations
4. Dirichlet series, Landau's theorem
5. Dirichlet's theorem
Chapter XI: The prime number theorem
1. The non-vanishing of ζ(1+it)
2. The Wiener-Ikehara theorem
3. The prime number theorem
A list of books
Notes
Subject index