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Basic Analytic Number Theory

  • Book
  • © 1993

Overview

Authors:
  1. Anatolij A. Karatsuba

    1. Steklov Mathematical Institute, Moscow, Russia

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  2. Melvyn B. Nathanson

    1. Institute for Advanced Study, School of Mathematics, Princeton, USA
      Department of Mathematics, Lehman College (CUNY), Bronx, USA

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Integer Points

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 1-26

  3. Entire Functions of Finite Order

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 27-40

  4. The Euler Gamma Function

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 41-50

  5. The Riemann Zeta Function

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 51-63

  6. The Connection Between the Sum of the Coefficients of a Dirichlet Series and the Function Defined by this Series

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 64-72

  7. The Method of I.M. Vinogradov in the Theory of the Zeta Function

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 73-93

  8. The Density of the Zeros of the Zeta Function and the Problem of the Distribution of Prime Numbers in Short Intervals

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 94-101

  9. Dirichlet L-Functions

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 102-121

  10. Prime Numbers in Arithmetic Progressions

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 122-140

  11. The Goldbach Conjecture

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 141-159

  12. Waring’s Problem

    • Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 160-180

  13. Back Matter

    Pages 181-222
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Keywords

About this book

This English translation of Karatsuba's Basic Analytic Number Theory follows closely the second Russian edition, published in Moscow in 1983. For the English edition, the author has considerably rewritten Chapter I, and has corrected various typographical and other minor errors throughout the the text. August, 1991 Melvyn B. Nathanson Introduction to the English Edition It gives me great pleasure that Springer-Verlag is publishing an English trans­ lation of my book. In the Soviet Union, the primary purpose of this monograph was to introduce mathematicians to the basic results and methods of analytic number theory, but the book has also been increasingly used as a textbook by graduate students in many different fields of mathematics. I hope that the English edition will be used in the same ways. I express my deep gratitude to Professor Melvyn B. Nathanson for his excellent translation and for much assistance in correcting errors in the original text. A.A. Karatsuba Introduction to the Second Russian Edition Number theory is the study of the properties of the integers. Analytic number theory is that part of number theory in which, besides purely number theoretic arguments, the methods of mathematical analysis play an essential role.

Authors and Affiliations

  • Steklov Mathematical Institute, Moscow, Russia

    Anatolij A. Karatsuba

  • Institute for Advanced Study, School of Mathematics, Princeton, USA

    Melvyn B. Nathanson

  • Department of Mathematics, Lehman College (CUNY), Bronx, USA

    Melvyn B. Nathanson

Bibliographic Information

  • Book Title: Basic Analytic Number Theory

  • Authors: Anatolij A. Karatsuba, Melvyn B. Nathanson

  • DOI: https://doi.org/10.1007/978-3-642-58018-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Hardcover ISBN: 978-3-540-53345-0Published: 14 December 1992

  • Softcover ISBN: 978-3-642-63436-9Published: 14 October 2012

  • eBook ISBN: 978-3-642-58018-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XIII, 222

  • Additional Information: Original Russian edition published by Publisher Nauka, Moscow, 1983

  • Topics: Number Theory

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