## 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 |

The Euclidean algorithm | 19 |

Chapter 3 | 52 |

Chapter 4 | 71 |

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 | |

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### Common terms and phrases

absolute convergence arithmetical function Assume asymptotic formula Bell series called coefficients common divisor completely multiplicative completes the proof complex numbers converges absolutely deduce defined Definition denote the number Dirichlet character mod Dirichlet product Dirichlet series Dirichlet's theorem divides divisor functions elements Example Exercises for Chapter exists functional equation given gives group G Hence identity implies induced modulus inequality infinitely many primes integers lattice points Lemma Let G linear congruence log log log2 logx Mobius function modp modulo multiplicative function nonnegative Note obtain odd prime partial sums partition polynomial congruence positive integers prime factors prime number theorem prime power primitive mod primitive root mod principal character quadratic nonresidue quadratic reciprocity law quadratic residues reduced residue system relation relatively prime residue classes residue system mod Riemann zeta function satisfies subgroup subset term theory unique values write