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Item Details
| Title:
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BASIC ANALYTIC NUMBER THEORY
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| By: |
A.A. Karatsuba, M.B. Nathanson (Trans) |
| Format: |
Hardback |
| List price:
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£76.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3540533451 |
| ISBN 13: |
9783540533450 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
19 November, 1992 |
| Pages: |
240 |
| Translated from: |
Russian |
| Description: |
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. |
| Synopsis: |
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. |
| Illustrations: |
8 figures |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Non-returnable |
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