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Basic Analytic Number Theory

  • Anatolij A. Karatsuba
  • Melvyn B. Nathanson

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 1-26
  3. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 27-40
  4. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 41-50
  5. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 51-63
  6. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 73-93
  7. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 102-121
  8. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 122-140
  9. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 141-159
  10. Anatolij A. Karatsuba, Melvyn B. Nathanson
    Pages 160-180
  11. Back Matter
    Pages 181-222

About this book

Introduction

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.

Keywords

Analytic Number Theory Analytische Zahlentheorie Distribution of prime numbers Goldbach's Problem Prime Prime number Waring's problem number theory the circle method

Authors and affiliations

  • Anatolij A. Karatsuba
    • 1
  • Melvyn B. Nathanson
    • 2
    • 3
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.Institute for Advanced StudySchool of MathematicsPrincetonUSA
  3. 3.Department of MathematicsLehman College (CUNY)BronxUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58018-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63436-9
  • Online ISBN 978-3-642-58018-5
  • Buy this book on publisher's site