Basic analytic number theory
Author(s)
Bibliographic Information
Basic analytic number theory
Springer-Verlag, c1993
- : us
- : gw
- Other Title
-
Osnovy analiticheskoĭ teorii chisel
Основы аналитической теории чисел
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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"