Anatoly A. Karatsuba's Books

The Riemann Zeta-Function

By: Anatoly A. Karatsuba,S. M. Voronin

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

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Page Count

409

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110886146

ISBN 13

9783110886146

Trigonometric Sums in Number Theory and Analysis

By: Gennady I. Arkhipov,Vladimir N. Chubarikov,Anatoly A. Karatsuba

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Trigonometric Sums in Number Theory and Analysis

By: Gennady I. Arkhipov,Vladimir N. Chubarikov,Anatoly A. Karatsuba

The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov ́s estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and in addition they present purely arithmetic results concerning the solvability of equations in integers.

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Page Count

565

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110197987

ISBN 13

9783110197983

Complex Analysis in Number Theory

By: Anatoly A. Karatsuba

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Complex Analysis in Number Theory

By: Anatoly A. Karatsuba

This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.

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Page Count

218

Publisher

CRC Press

Published Date

ISBN 10

0849328667

ISBN 13

9780849328664

Book's by Anatoly A. Karatsuba

The Riemann Zeta-Function

The Riemann Zeta-Function

Trigonometric Sums in Number Theory and Analysis

Trigonometric Sums in Number Theory and Analysis

Complex Analysis in Number Theory

Complex Analysis in Number Theory

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