Cover Image

Basic analytic number theory /

Show other versions (1)

This book provides an introduction to four central problems in analytic number theory. These are (1) the problem of estimating the number of integerpoints in planar domains (2) the problem of the distribution of prime numbers in the sequence of all natural numbers and in arithmetic progressions (3)...

Full description

Bibliographic Details
Main Author: Karat︠s︡uba, Anatoliĭ Alekseevich
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin ; New York : Springer-Verlag, [1993]
Subjects:
Number theory.
problème Waring.
conjecture Goldbach.
progression arithmétique.
fonction Dirichlet.
nombre premier.
distribution.
méthode Vinogradov.
série Dirichlet.
Fonction zéta.
fonction gamma.
fonction Euler.
fonction entière.
point entier.
théorie nombre.
Getaltheorie.
Nombres, Théorie des.
Electronic books.
Online Access:Connect to the full text of this electronic book
Description
Summary:This book provides an introduction to four central problems in analytic number theory. These are (1) the problem of estimating the number of integerpoints 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 problem on sums of primes, and (4) Waring's problem on sums of k-th powers. To solve these problems, one uses the fundamental methods of analytic number theory: 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. The mathematical prerequisites for this volume are undergraduate courses in number theroy, mathematical analysis, and complex variables. The book would be an excellent text for a one or two semester course in analytic number theory for advanced undergraduates or graduate students.
Item Description:Translation of: Osnovy analiticheskoĭ teorii chisel.
Electronic resource.
Physical Description:1 online resource (xiii, 222 pages) : illustrations
Format:Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Bibliography:Includes bibliographical references (page [219]) and index.
ISBN:9783642580185 (electronic bk.)
3642580181 (electronic bk.)