Basic Analytic Number Theory
Anatolij A. Karatsuba(Author)
Springer (Publisher)
Published in 1993
Book
Hardback
XIII, 222 pages
978-3-540-53345-0 (ISBN)
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.
More details
Language
English
Place of publication
Berlin
Germany
Target group
College/higher education
Professional and scholarly
Illustrations
8 figs.
Weight
515 gr
ISBN-13
978-3-540-53345-0 (9783540533450)
Schweitzer Classification
Other editions
Additional editions

Anatolij A. Karatsuba
Basic Analytic Number Theory
Book
10/2012
Springer
€85.59
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