Basic analytic number theory

書誌事項

Basic analytic number theory

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

Springer-Verlag, c1993

  • : us
  • : gw

タイトル別名

Osnovy analiticheskoĭ teorii chisel

Основы аналитической теории чисел

大学図書館所蔵 件 / 55

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注記

Translation of: Osnovy analiticheskoĭ teorii chisel

Includes bibliographical references and index

内容説明・目次

内容説明

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.

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詳細情報

  • NII書誌ID(NCID)
    BA1908729X
  • ISBN
    • 0387533451
    • 3540533451
  • LCCN
    91040715
  • 出版国コード
    gw
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    rus
  • 出版地
    Berlin ; New York
  • ページ数/冊数
    xiii, 222 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
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