## Introduction to Analytic Number Theory, Volume 1to Analytic Number Theory With 24 Illustrations Springer Tom M. Apostol Department of Mathematics California Institute ofTechnology Pasadena, California 91125 U.S.A. Editorial Board S. Axler F.W. Gehring K.A. Ribet Mathematics Department Mathematics Department Mathematics Department San Francisco State East Hali University of California, University University of Michigan at Berkeley San Francisco, CA 94132 Ann Arbor, MI 48109 Berkeley, CA 94720-3840 USA USA USA Mathematics Subject Classification (2000): 11-01, Il AXX Library of Congress Cataloging-in-Publication Data Apostol, Tom M. lntroduction to analytic number theory. (Undergraduate texts in mathematics) "Evolved from a course (Mathematics 160) offered at the California Institute ofTechnology during the last 25 years." Bibliography: p. 329. lncludes index. 1. Numbers, Theory of. 2. Arithmetic functions. 3. Numbers, Prime. !. Title. Printed on acid-frec paper. QA24l.A6 512 '73 75-3 7697 ISBN 978-1-4419-2805-4 ISBN 978-1-4757-5579-4 (eBook) DOI 10.1007/978-1-4757-5579-4 (c) 1976 Springer Science+Business Media New York Originally published by Springer Science+Business Media, Inc. in 1976 AII rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher Springer Science+Business Media, LLC, except for brief excerpts in connection with reviews or scho1arly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimi1ar methodology now known or hereafter developed is forbidden. |

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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.

#### Review: Introduction to Analytic Number Theory

User Review - Elizabeth SQ Goodman - GoodreadsI figure I need some grounding in analytic number theory, because I've always found it confusing. I read the first two chapters or so of this and that was fine. Read full review

### 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