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Introduction to Analytic Number Theory

  • Textbook
  • © 1976

Overview

Authors:
  1. Tom M. Apostol

    1. Department of Mathematics, California Institute of Technology, Pasadena, USA

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Historical Introduction

    • Tom M. Apostol
    Pages 1-12

  3. The Fundamental Theorem of Arithmetic

    • Tom M. Apostol
    Pages 13-23

  4. Arithmetical Functions and Dirichlet Multiplication

    • Tom M. Apostol
    Pages 24-51

  5. Averages of Arithmetical Functions

    • Tom M. Apostol
    Pages 52-73

  6. Some Elementary Theorems on the Distribution of Prime Numbers

    • Tom M. Apostol
    Pages 74-105

  7. Congruences

    • Tom M. Apostol
    Pages 106-128

  8. Finite Abelian Groups and Their Characters

    • Tom M. Apostol
    Pages 129-145

  9. Dirichlet’s Theorem on Primes in Arithmetical Progressions

    • Tom M. Apostol
    Pages 146-156

  10. Periodic Arithmetical Functions and Gauss Sums

    • Tom M. Apostol
    Pages 157-177

  11. Quadratic Residues and the Quadratic Reciprocity Law

    • Tom M. Apostol
    Pages 178-203

  12. Primitive Roots

    • Tom M. Apostol
    Pages 204-223

  13. Dirichlet Series and Euler Products

    • Tom M. Apostol
    Pages 224-248

  14. The Functions ζ(s) and L(s, χ)

    • Tom M. Apostol
    Pages 249-277

  15. Analytic Proof of the Prime Number Theorem

    • Tom M. Apostol
    Pages 278-303

  16. Partitions

    • Tom M. Apostol
    Pages 304-328

  17. Back Matter

    Pages 329-340
    Download chapter PDF
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Reviews

From the reviews:

T.M. Apostol

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. The presentation is invariably lucid and the book is a real pleasure to read."

—MATHEMATICAL REVIEWS

“After reading Introduction to Analytic Number Theory one is left with the impression that the author, Tom M. Apostal, has pulled off some magic trick. … I must admit that I love this book. The selection of topics is excellent, the exposition is fluid, the proofs are clear and nicely structured, and every chapter contains itsown set of … exercises. … this book is very readable and approachable, and it would work very nicely as a text for a second course in number theory.” (Álvaro Lozano-Robledo, The Mathematical Association of America, December, 2011)

Authors and Affiliations

  • Department of Mathematics, California Institute of Technology, Pasadena, USA

    Tom M. Apostol

Bibliographic Information

  • Book Title: Introduction to Analytic Number Theory

  • Authors: Tom M. Apostol

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-5579-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1976

  • Hardcover ISBN: 978-0-387-90163-3Published: 11 May 1976

  • Softcover ISBN: 978-1-4419-2805-4Published: 01 December 2010

  • eBook ISBN: 978-1-4757-5579-4Published: 29 June 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XII, 340

  • Topics: Number Theory

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