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Exponential Sums and their Applications : Mathematics and its Applications - N.M. Korobov

Exponential Sums and their Applications

Mathematics and its Applications

Hardcover Published: 31st March 1992
ISBN: 9780792316473
Number Of Pages: 210

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The method of exponential sums is a general method enabling the solution of a wide range of problems in the theory of numbers and its applications. This volume presents an exposition of the fundamentals of the theory with the help of examples which show how exponential sums arise and how they are applied in problems of number theory and its applications.
The material is divided into three chapters which embrace the classical results of Gauss, and the methods of Weyl, Mordell and Vinogradov; the traditional applications of exponential sums to the distribution of fractional parts, the estimation of the Riemann zeta function; and the theory of congruences and Diophantine equations. Some new applications of exponential sums are also included.
It is assumed that the reader has a knowledge of the fundamentals of mathematical analysis and of elementary number theory.

Series Editor's Preface
Complete Exponential Sumsp. 1
Sums of the first degreep. 1
General properties of complete sumsp. 7
Gaussian sumsp. 13
Simplest complete sumsp. 22
Mordell's methodp. 29
Systems of congruencesp. 34
Sums with exponential functionp. 40
Distribution of digits in complete period of periodic fractionsp. 45
Exponential sums with recurrent functionp. 53
Sums of Legendre's symbolsp. 61
Weyl's Sumsp. 68
Weyl's methodp. 68
Systems of equationsp. 78
Vinogradov's mean value theoremp. 87
Estimates of Weyl's sumsp. 97
Repeated application of the mean value theoremp. 110
Sums arising in zeta-function theoryp. 119
Incomplete rational sumsp. 126
Double exponential sumsp. 133
Uniform distribution of fractional partsp. 139
Fractional Parts Distribution, Normal Numbers, and Quadrature Formulasp. 139
Uniform distribution of fractional partsp. 139
Uniform distribution of functions systems and completely uniform distributionp. 149
Normal and conjunctly normal numbersp. 159
Distribution of digits in period part of periodical fractionsp. 166
Connection between exponential sums, quadrature formulas and fractional parts distributionp. 176
Quadrature and interpolation formulas with the number-theoretical netsp. 187
Referencesp. 203
Subject Indexp. 207
Index of Namesp. 209
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792316473
ISBN-10: 0792316479
Series: Mathematics and its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 210
Published: 31st March 1992
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.5

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