Basic analytic number theory
著者
書誌事項
Basic analytic number theory
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 全54件
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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