Basic Analytic Number Theory [Hardcover] Karatsuba, Anatolij A. and Nathanson, M.B.

Karatsuba, Anatolij A.

ISBN 10: 3540533451 / ISBN 13: 9783540533450

Editore: Springer, 1992

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Slight knock to lower outer corner of rear cover. Content in almost mint condition.

Codice articolo 105669-4

Dati bibliografici

• Titolo: Basic Analytic Number Theory [Hardcover] Karatsuba, Anatolij A. and Nathanson, M.B.
• Editore: Springer
• Data di pubblicazione: 1992
• Lingua: Inglese
• ISBN 10: 3540533451
• ISBN 13: 9783540533450
• Rilegatura: Rilegato
• Condizione: Very Good

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Riassunto

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.