## Introduction to Analytic Number Theory"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS |

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解析数论概论，研一下教材

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I've found this to be the best overall introduction to analytic number theory. I'm trained in physics, and interested in number theory, and this book really helped me to learn the basics. The problems are excellent as well.

### Contents

Historical Introduction | 1 |

The Fundamental Theorem of Arithmetic | 13 |

Chapter | 14 |

Chapter 2 | 24 |

Chapter 3 | 47 |

Chapter 4 | 74 |

Chapter 5 | 106 |

Chapter 6 | 129 |

Chapter 9 | 177 |

Primitive Roots | 204 |

Chapter 11 | 223 |

Chapter 12 | 249 |

Chapter 13 | 278 |

Partitions | 304 |

329 | |

335 | |

### Other editions - View all

Introduction to Analytic Number Theory, Volume 1 Tom M. Apostol,TOM M AUTOR APOSTOL No preview available - 1976 |

### Common terms and phrases

analytic apply arithmetical function Assume asymptotic formula bounded called character mod coefficients common completely completely multiplicative completes the proof congruence consider constant converges converges absolutely deduce defined Definition denote derivative determine Dirichlet series distinct divides divisible divisor elements equal equation equivalent Euler's exactly example Exercises for Chapter exists expressed extended fact Figure finite formula given gives half-plane Hence holds identity implies induced modulus inequality infinitely inverse lattice points Lemma linear log x mod k modulo multiplicative Note obtain odd prime periodic polynomial polynomial congruence positive integers power series prime number theorem primitive root mod PROOF properties prove relation relatively prime result satisfies solutions square subgroup term Theorem theory unique values write zeta function Σ Σ