Preface to the Second Edition
Acknowledgments for the Second Edition
Preface to the First Edition
Acknowledgments for the First Edition
I  Problems
1  Arithmetic Functions
  1.1  The Mobius Inversion Formula and Applications
  1.2  Formal Dirichlet Series
  1.3  Orders of Some Arithmetical Functions
  1.4  Average Orders of Arithmetical Functions
  1.5  Supplementary Problems
2  Primes in Arithmetic Progressions
  2.1  Summation Techniques
  2.2  Characters mod q
  2.3  Dirichlet's Theorem
  2.4  Dirichlet's Hyperbola Method
  2.5  Supplementary Problems
3  The Prime Number Theorem
  3.1  Chebyshev's Theorem
  3.2  Nonvanishing of Dirichlet Series on Re(s) = 1
  3.3  The Ikehara - Wiener Theorem
  3.4  Supplementary Problems
4  The Method of Contour Integration
  4.1  Some Basic Integrals
  4.2  The Prime Number Theorem
  4.3  Further Examples
  4.4  Supplementary Problems
5  Functional Equations
  5.1  Poisson's Summation Formula
  5.2  The Riemann Zeta Function
  5.3  Gauss Sums
  5.4  Dirichlet L-functions
  5.5  Supplementary Problems
6  Hadamard Products
  6.1  Jensen's Theorem
  6.2  Entire Functions of Order I
  6.3  The Gamma Function
  6.4  Infinite Products for ξ(s) and ξ(s, X)
  6.5  Zero-Free Regions for □(s) and G(s, X)
  6.6  Supplementary Problems
7  Explicit Formulas
  7.1  Counting Zeros
  7.2  Explicit Formula for ψ(x)
  7.3  Weil's Explicit Formula
  7.4  Supplementary Problems
8  The Selberg Class
  8.1  The Phragmen- Lindelof Theorem
  8.2  Basic Properties
  8.3  Selberg's Conjectures
  8.4  Supplementary Problems
9  Sieve Methods
  9.1  The Sieve of Eratosthenes
  9.2  Brun's Elementary Sieve
  9.3  Selberg's Sieve
  9.4  Supplementary Problems
10  p-adic Methods
  10.10strowski's Theorem
  10.2 Hensel's Lemma
  10.3 p-adic Interpolation
  10.4 The p-adic Zeta-Function
  10.5 Supplementary Problems
11  Equidistribution
  11.1 Uniform distribution modulo 1
  11.2 Normal numbers
  11.3 Asymptotic distribution functions mod 1
  11.4 Discrepancy
  11.5 Equidistribution and L-functions
  11.6 Supplementary Problems
II  Solutions
1  Arithmetic Functions
  1.1  The Mobius Inversion Formula and Applications
  1.2  Formal Dirichlet Series
  1.3  Orders of Some Arithmetical Functions
  1.4  Average Orders of Arithmetical Functions
  1.5  Supplementary Problems
2  Primes in Arithmetic Progressions
  2.1  Characters mod q
  2.2  Dirichlet's Theorem
  2.3  Dirichlet's Hyperbola Method
  2.4  Supplementary Problems
3  The Prime Number Theorem
  3.1  Chebyshev's Theorem
  3.2  Nonvanishing of Dirichlet Series on Re(s) = 1
  3.3  The Ikehara - Wiener Theorem
  3.4  Supplementary Problems
4  The Method of Contour Integration
  4.1  Some Basic Integrals
  4.2  The Prime Number Theorem
  4.3  Further Examples
  4.4  Supplementary Problems
5  Functional Equations
  5.1  Poisson's Summation Formula
  5.2  The Riemann Zeta Function
  5.3  Gauss Sums
  5.4  Dirichlet L-functions
  5.5  Supplementary Problems
6  Hadamard Products
  6.1  Jensen's theorem
  6.2  The Gamma Function
  6.3  Infinite Products for ξ(s) and ξ(s, X)
  6.4  Zero-Free Regions for □(s) and L(s, X)
  6.5  Supplementary Problems
7  Explicit Formulas
  7.1  Counting Zeros
  7.2  Explicit Formula for ψ(x)
  7.3  Supplementary Problems
8  The Selberg Class
  8.1  The Phragmen - Lindelof Theorem
  8.2  Basic Properties
  8.3  Selberg's Conjectures
  8.4  Supplementary Problems
9  Sieve Methods
  9.1  The Sieve of Eratosthenes
  9.2  Brun's Elementary Sieve
  9.3  Selberg's Sieve
  9.4  Supplementary Problems
10 p-adic Methods
  10.10strowski's Theorem
  10.2 Hensel's Lemma
  10.3 p-adic Interpolation
  10.4 The p-adic □-Function
  10.5 Supplementary Problems
11 Equidistribution
  11.1 Uniform distribution modulo I
  11.2 Normal numbers
  11.3 Asymptotic distribution functions mod 1
  11.4 Discrepancy
  11.5 Equidistribution and L-functio