| Preface to the Second Edition | p. vii |
| Acknowledgments for the Second Edition | p. ix |
| Preface to the First Edition | p. xi |
| Acknowledgments for the First Edition | p. xv |
| Problems | p. 1 |
| Arithmetic Functions | p. 3 |
| The M&duml;bius Inversion Formula and Applications | p. 4 |
| Formal Dirichlet Series | p. 7 |
| Orders of Some Arithmetical Functions | p. 9 |
| Average Orders of Arithmetical Functions | p. 10 |
| Supplementary Problems | p. 11 |
| Primes in Arithmetic Progressions | p. 17 |
| Summation Techniques | p. 17 |
| Characters mod q | p. 22 |
| Dirichlet's Theorem | p. 24 |
| Dirichlet's Hyperbola Method | p. 27 |
| Supplementary Problems | p. 29 |
| The Prime Number Theorem | p. 35 |
| Chebyshev's Theorem | p. 36 |
| Nonvanishing of Dirichlet Series on Re(s)=1 | p. 39 |
| The Ikehara - Wiener Theorem | p. 42 |
| Supplementary Problems | p. 48 |
| The Method of Contour Integration | p. 53 |
| Some Basic Integrals | p. 53 |
| The Prime Number Theorem | p. 57 |
| Further Examples | p. 62 |
| Supplementary Problems | p. 65 |
| Functional Equations | p. 69 |
| Poisson's Summation Formula | p. 69 |
| The Riemann Zeta Function | p. 72 |
| Gauss Sums | p. 75 |
| Dirichlet L-functions | p. 76 |
| Supplementary Problems | p. 79 |
| Hadamard Products | p. 85 |
| Jensen's Theorem | p. 85 |
| Entire Functions of Order 1 | p. 88 |
| The Gamma Function | p. 91 |
| Infinite Products for (s) and (s,x) | p. 93 |
| Zero-Free Regions for (s) and L(s,x) | p. 94 |
| Supplementary Problems | p. 99 |
| Explicit Formulas | p. 101 |
| Counting Zeros | p. 101 |
| Explicit Formula for (x) | p. 104 |
| Weil's Explicit Formula | p. 107 |
| Supplementary Problems | p. 110 |
| The Selberg Class | p. 115 |
| The Phragmén - Lindeloüf Theorem | p. 116 |
| Basic Properties | p. 118 |
| Selberg's Conjectures | p. 123 |
| Supplementary Problems | p. 125 |
| Sieve Methods | p. 127 |
| The Sieve of Eratosthenes | p. 127 |
| Brun's Elementary Sieve | p. 133 |
| Selberg's Sieve | p. 138 |
| Supplementary Problems | p. 144 |
| p-adic Methods | p. 147 |
| Ostrowski's Theorem | p. 147 |
| Hensel's Lemma | p. 155 |
| p-adic Interpolation | p. 159 |
| The p-adic Zeta-Function | p. 165 |
| Supplementary Problems | p. 168 |
| Equidistribution | p. 171 |
| Uniform distribution modulo 1 | p. 171 |
| Normal numbers | p. 177 |
| Asymptotic distribution functions mod 1 | p. 180 |
| Discrepancy | p. 182 |
| Equidistribution and L-functions | p. 189 |
| Supplementary Problems | p. 193 |
| Solutions | p. 197 |
| Arithmetic Functions | p. 199 |
| The Möbius Inversion Formula and Applications | p. 199 |
| Formal Dirichlet Series | p. 208 |
| Orders of Some Arithmetical Functions | p. 212 |
| Average Orders of Arithmetical Functions | p. 215 |
| Supplementary Problems | p. 220 |
| Primes in Arithmetic Progressions | p. 237 |
| Characters mod q | p. 237 |
| Dirichlet's Theorem | p. 246 |
| Dirichlet's Hyperbola Method | p. 251 |
| Supplementary Problems | p. 257 |
| The Prime Number Theorem | p. 273 |
| Chebyshev's Theorem | p. 273 |
| Nonvanishing of Dirichlet Series on Re(s)=1 | p. 280 |
| The Ikehara - Wiener Theorem | p. 288 |
| Supplementary Problems | p. 292 |
| The Method of Contour Integration | p. 305 |
| Some Basic Integrals | p. 305 |
| The Prime Number Theorem | p. 311 |
| Further Examples | p. 314 |
| Supplementary Problems | p. 317 |
| Functional Equations | p. 329 |
| Poisson's Summation Formula | p. 329 |
| The Riemann Zeta Function | p. 332 |
| Gauss Sums | p. 333 |
| Dirichlet L-functions | p. 335 |
| Supplementary Problems | p. 338 |
| Hadamard Products | p. 357 |
| Jensen's Theorem | p. 357 |
| The Gamma Function | p. 358 |
| Infinite Products for (s) and (s,x) | p. 369 |
| Zero-Free Regions for (s) and L(s,x) | p. 374 |
| Supplementary Problems | p. 379 |
| Explicit Formulas | p. 385 |
| Counting Zeros | p. 385 |
| Explicit Formula for (x) | p. 388 |
| Supplementary Problems | p. 393 |
| The Selberg Class | p. 403 |
| The Phragmén - Lindeloüf Theorem | p. 403 |
| Basic Properties | p. 404 |
| Selberg's Conjectures | p. 411 |
| Supplementary Problems | p. 417 |
| Sieve Methods | p. 423 |
| The Sieve of Eratosthenes | p. 423 |
| Brun's Elementary Sieve | p. 429 |
| Selberg's Sieve | p. 432 |
| Supplementary Problems | p. 439 |
| p-adic Methods | p. 449 |
| Ostrowski's Theorem | p. 449 |
| Hensel's Lemma | p. 454 |
| p-adic Interpolation | p. 456 |
| The p-adic -Function | p. 463 |
| Supplementary Problems | p. 468 |
| Equidistribution | p. 475 |
| Uniform distribution modulo 1 | p. 475 |
| Normal numbers | p. 483 |
| Asymptotic distribution functions mod 1 | p. 484 |
| Discrepancy | p. 485 |
| Equidistribution and L-functions | p. 488 |
| Supplementary Problems | p. 490 |
| References | p. 497 |
| Index | p. 499 |
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