## Introduction to Analytic Number Theory, Volume 1This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet L-functions. Also included is an introduction to partitions. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus. |

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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 | |

### 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