Exponential Sums And Their Applications

Author : N.M Korobov
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 41,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401580328

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Exponential Sums and their Applications by N.M Korobov Pdf

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.

Author : G. R. H. Greaves,G. Harman,M. N. Huxley
Publisher : Cambridge University Press
Page : 360 pages
File Size : 51,5 Mb
Release : 1997-01-30
Category : Mathematics
ISBN : 9780521589574

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Sieve Methods, Exponential Sums, and Their Applications in Number Theory by G. R. H. Greaves,G. Harman,M. N. Huxley Pdf

State-of-the-art analytic number theory proceedings.

Author : G. R. H. Greaves,G. Harman,M. N. Huxley
Publisher : Unknown
Page : 360 pages
File Size : 51,6 Mb
Release : 1997
Category : Electronic books
ISBN : 110736745X

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Sieve Methods, Exponential Sums, and Their Applications in Number Theory by G. R. H. Greaves,G. Harman,M. N. Huxley Pdf

State-of-the-art analytic number theory proceedings.

Author : Ping Ding
Publisher : National Library of Canada = Bibliothèque nationale du Canada
Page : 168 pages
File Size : 50,8 Mb
Release : 1993
Category : Exponential sums
ISBN : 0315911360

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Exponential Sums and Applications [microform] by Ping Ding Pdf

Author : Andrei Raigorodskii,Michael Th. Rassias
Publisher : Springer Nature
Page : 313 pages
File Size : 48,8 Mb
Release : 2020-03-11
Category : Mathematics
ISBN : 9783030379049

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Trigonometric Sums and Their Applications by Andrei Raigorodskii,Michael Th. Rassias Pdf

This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.

Author : S. W. Graham,G. Kolesnik
Publisher : Cambridge University Press
Page : 133 pages
File Size : 44,6 Mb
Release : 1991-01-25
Category : Mathematics
ISBN : 9780521339278

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Van Der Corput's Method of Exponential Sums by S. W. Graham,G. Kolesnik Pdf

This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professionals in analytic number theory. The authors show how the method can be applied to problems such as upper bounds for the Riemann-Zeta function. the Dirichlet divisor problem, the distribution of square free numbers, and the Piatetski-Shapiro prime number theorem.

Author : Sergei Konyagin,Igor Shparlinski
Publisher : Penguin Group
Page : 182 pages
File Size : 41,8 Mb
Release : 1999-09-02
Category : Computers
ISBN : 0521642639

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Character Sums with Exponential Functions and Their Applications by Sergei Konyagin,Igor Shparlinski Pdf

A treatment of a lively topic from number theory for graduate students and researchers.

Author : Michel Lavrauw
Publisher : American Mathematical Soc.
Page : 204 pages
File Size : 45,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821852989

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Theory and Applications of Finite Fields by Michel Lavrauw Pdf

This volume contains the proceedings of the 10th International Congress on Finite Fields and their Applications (Fq 10), held July 11-15, 2011, in Ghent, Belgium. Research on finite fields and their practical applications continues to flourish. This volume's topics, which include finite geometry, finite semifields, bent functions, polynomial theory, designs, and function fields, show the variety of research in this area and prove the tremendous importance of finite field theory.

Author : Dieter Jungnickel,H. Niederreiter
Publisher : Springer Science & Business Media
Page : 500 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642567551

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Finite Fields and Applications by Dieter Jungnickel,H. Niederreiter Pdf

This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (

Author : M. N. Huxley
Publisher : Clarendon Press
Page : 510 pages
File Size : 50,6 Mb
Release : 1996-06-13
Category : Mathematics
ISBN : 9780191590320

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Area, Lattice Points, and Exponential Sums by M. N. Huxley Pdf

In analytic number theory a large number of problems can be "reduced" to problems involving the estimation of exponential sums in one or several variables. This book is a thorough treatment of the developments arising from the method developed by Bombieri and Iwaniec in 1986 for estimating the Riemann zeta function on the line *s = 1/2. Huxley and his coworkers (mostly Huxley) have taken this method and vastly extended and improved it. The powerful techniques presented here go considerably beyond older methods for estimating exponential sums such as van de Corput's method. The potential for the method is far from being exhausted, and there is considerable motivation for other researchers to try to master this subject. However, anyone currently trying to learn all of this material has the formidable task of wading through numerous papers in the literature. This book simplifies that task by presenting all of the relevant literature and a good part of the background in one package. The audience for the book will be mathematics graduate students and faculties with a research interest in analytic theory; more specifically, those with an interest in exponential sum methods. The book is self-contained; any graduate student with a one semester course in analytic number theory should have a more than sufficient background.

Author : Taekyun Kim
Publisher : MDPI
Page : 238 pages
File Size : 52,6 Mb
Release : 2019-10-15
Category : Mathematics
ISBN : 9783039216208

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Current Trends in Symmetric Polynomials with their Applications by Taekyun Kim Pdf

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Author : Matti I. Jutila
Publisher : Springer
Page : 138 pages
File Size : 45,5 Mb
Release : 1988-02-19
Category : Mathematics
ISBN : 3540183663

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Lectures on a Method in the Theory of Exponential Sums by Matti I. Jutila Pdf

These notes are based on the lectures given by the author at the Tata Institute in 1985 on certain classes of exponential sums and their applications in analytic number theory. More specifically, the exponential sums under consideration involve either the divisor function d(n) or Fourier coefficients of cusp forms (e.g. Ramanujan's function #3(n)). However, the "transformation method" presented, relying on general principles such as functional equations, summation formulae and the saddle point method, has a wider scope. Its classical analogue is the familiar "process B" in van der Corput's method, that transforms ordinary exponential sums by Poisson's summation formula and the saddle point method. In the present context, the summation formulae required are of the Voronoi type. These are derived in Chapter I. Chapter II deals with exponential integrals and the saddle point method. The main results of these notes, the general transformation formulae for exponential sums, are then established in Chapter III and some applications are given in Chapter IV. First the transformation of Dirichlet polynomials is worked out in detail, and the rest of the chapter is devoted to estimations of exponential sums and Dirichlet series. The material in Chapters III and IV appears here for the first time in print. The notes are addressed to researchers but are also accessible to graduate students with some basic knowledge of analytic number theory.

Author : Harald Niederreiter
Publisher : World Scientific
Page : 460 pages
File Size : 44,9 Mb
Release : 2002-12-03
Category : Mathematics
ISBN : 9789814487665

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Coding Theory and Cryptology by Harald Niederreiter Pdf

The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security. Contents:Extremal Problems of Coding Theory (A Barg)Analysis and Design Issues for Synchronous Stream Ciphers (E Dawson & L Simpson)Quantum Error-Correcting Codes (K Feng)Public Key Infrastructures (D Gollmann)Computational Methods in Public Key Cryptology (A K Lenstra)Detecting and Revoking Compromised Keys (T Matsumoto)Algebraic Function Fields Over Finite Fields (H Niederreiter)Authentication Schemes (D Y Pei)Exponential Sums in Coding Theory, Cryptology and Algorithms (I E Shparlinski)Distributed Authorization: Principles and Practice (V Varadharajan)Introduction to Algebraic Geometry Codes (C P Xing) Readership: Graduate students and researchers in number theory, discrete mathematics, coding theory, cryptology and IT security. Keywords:Coding Theory;Cryptology;Number Theory;Algebraic-Geometry Codes;Public-Key Infrastructures;Error-Correcting Codes

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512886

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Author : Tor Helleseth,Dilip Sarwate,Hong-Yeop Song,Kyeongcheol Yang
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 50,8 Mb
Release : 2005-06
Category : Computers
ISBN : 9783540260844

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Sequences and Their Applications - SETA 2004 by Tor Helleseth,Dilip Sarwate,Hong-Yeop Song,Kyeongcheol Yang Pdf

This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Sequences and Their Applications, SETA 2004, held in Seoul, Korea in October 2004. The 30 revised full papers presented together with 4 invited survey articles were carefully selected during two rounds of reviewing and improvement from initially 59 submissions. The papers are organized in topical sections on complexity of sequences, perfect sequences, sequence construction, sequences modulo z, sequence generator properties and applications, multi-dimensional sequences, optics and OFDM applications, and polynomials and functions.