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Introduction to Analytic Number Theory

  • Book
  • © 1968

Overview

Authors:
  1. K. Chandrasekharan

    1. Eidgenössische Technische Hochschule Zürich, Switzerland

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 148)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-VIII
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  2. The unique factorization theorem

    • K. Chandrasekharan
    Pages 1-10

  3. Congruences

    • K. Chandrasekharan
    Pages 11-17

  4. Rational approximation of irrationals and Hurwitz’s theorem

    • K. Chandrasekharan
    Pages 18-25

  5. Quadratic residues and the representation of a number as a sum of four squares

    • K. Chandrasekharan
    Pages 26-33

  6. The law of quadratic reciprocity

    • K. Chandrasekharan
    Pages 34-44

  7. Arithmetical functions and lattice points

    • K. Chandrasekharan
    Pages 45-62

  8. Chebyshev’s theorem on the distribution of prime numbers

    • K. Chandrasekharan
    Pages 63-83

  9. Weyl’s theorems on uniform distribution and Kronecker’s theorem

    • K. Chandrasekharan
    Pages 84-96

  10. Minkowski’s theorem on lattice points in convex sets

    • K. Chandrasekharan
    Pages 97-104

  11. Dirichlet’s theorem on primes in an arithmetical progression

    • K. Chandrasekharan
    Pages 105-121

  12. The prime number theorem

    • K. Chandrasekharan
    Pages 122-130

  13. Back Matter

    Pages 131-143
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Keywords

About this book

This book has grown out of a course of lectures I have given at the Eidgenossische Technische Hochschule, Zurich. Notes of those lectures, prepared for the most part by assistants, have appeared in German. This book follows the same general plan as those notes, though in style, and in text (for instance, Chapters III, V, VIII), and in attention to detail, it is rather different. Its purpose is to introduce the non-specialist to some of the fundamental results in the theory of numbers, to show how analytical methods of proof fit into the theory, and to prepare the ground for a subsequent inquiry into deeper questions. It is pub­ lished in this series because of the interest evinced by Professor Beno Eckmann. I have to acknowledge my indebtedness to Professor Carl Ludwig Siegel, who has read the book, both in manuscript and in print, and made a number of valuable criticisms and suggestions. Professor Raghavan Narasimhan has helped me, time and again, with illuminating comments. Dr. Harold Diamond has read the proofs, and helped me to remove obscurities. I have to thank them all. K.C.

Authors and Affiliations

  • Eidgenössische Technische Hochschule Zürich, Switzerland

    K. Chandrasekharan

Bibliographic Information

  • Book Title: Introduction to Analytic Number Theory

  • Authors: K. Chandrasekharan

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-46124-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1968

  • Softcover ISBN: 978-3-642-46126-2Published: 01 March 2012

  • eBook ISBN: 978-3-642-46124-8Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: VIII, 144

  • Topics: Number Theory

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