Basic Analytic Number Theory

A.A. Karatsuba

ISBN 10: 3540533451 / ISBN 13: 9783540533450

Published by Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE, 1993

About this Item

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.

Seller Inventory # LU-9783540533450

Bibliographic Details

• Title: Basic Analytic Number Theory
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE
• Publication Date: 1993
• Language: English
• ISBN 10: 3540533451
• ISBN 13: 9783540533450
• Binding: Hardback
• Edition: Illustrated.
• Condition: New
• Dimensions: 15.6W x 1.42H x 23.39D centimeters 15.6 centimeters width by 1.42 centimeters height by 23.39 centimeters depth
• Weight: 515 grams

About this title

Synopsis

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.

Language Notes

Text: English (translation)
Original Language: Russian