Basic analytic number theory

Author(s)

• Karat︠s︡uba, Anatoliĭ Alekseevich

Bibliographic Information

Basic analytic number theory

Anatolij A. Karatsuba ; translated from the Russian by Melvyn B. Nathanson

Springer-Verlag, c1993

• : us
• : gw

Other Title

Osnovy analiticheskoĭ teorii chisel

Основы аналитической теории чисел

Note

Translation of: Osnovy analiticheskoĭ teorii chisel

Includes bibliographical references and index

Description and Table of Contents

Description

This work provides an introduction to four central problems in analytic number theory. These are (1) the problems of estimating the number of integer points in planar domains, (2) the problem of the distribution of prime numbers in the sequence of all natural numbers and in arithmetic progressions, (3) Goldbach's problems on sums of primes, and (4) Waring's problem on sums of k-th powers. The following fundamental methods of analytic number theory are used to solve these problems: complex integration, I.M. Vinogradov's method of trigonometric sums, and the circle method of G.H. Hardy, J.E. Littlewood, and S. Ramanujan. There are numerous exercises at the end of each chapter. These exercises either refine the theorems proved in the text, or lead to new ideas in number theory. The author also includes a section of hints for the solution of the exercises.

by "Nielsen BookData"

Details

• NCID: BA1908729X
• ISBN:
  • 0387533451
  • 3540533451
• LCCN: 91040715
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: rus
• Place of Publication: Berlin ; New York
• Pages/Volumes: xiii, 222 p.
• Size: 24 cm
• Classification:
  • LCC : QA241
  • DC20 : 512/.73
  • NDC8 : 412.3
• Subject Headings:
  • LCSH : Number theory