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Basic Analytic Number Theory - Anatolij A. Karatsuba

Basic Analytic Number Theory

XIII, 222 Seiten
1993
Springer Berlin (Hersteller)
978-3-540-53345-0 (ISBN)
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Translator: Nathanson, M.B.
Introduces four problems in analytic number theory: that of estimating the number of integer points in planar domains; that of the distribution of prime numbers in the sequence of all natural numbers and in arithmetic progressions; Goldbach's problems on sums of primes; and Waring's problem.

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.
Übersetzer M. B. Nathansou
Zusatzinfo 8 figs.
Sprache englisch
Gewicht 516 g
Einbandart gebunden
Schlagworte Zahlentheorie
ISBN-10 3-540-53345-1 / 3540533451
ISBN-13 978-3-540-53345-0 / 9783540533450
Zustand Neuware
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