Exponential Sums And Applications Microform

Author : N.M Korobov
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 52,9 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 : Unknown
Page : 360 pages
File Size : 54,6 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 : G. R. H. Greaves,G. Harman,M. N. Huxley
Publisher : Cambridge University Press
Page : 360 pages
File Size : 47,8 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 : Matti I. Jutila
Publisher : Springer
Page : 138 pages
File Size : 48,7 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 : Sergei Konyagin,Igor Shparlinski
Publisher : Penguin Group
Page : 182 pages
File Size : 40,5 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 : KonUL.
Publisher : Unknown
Page : 163 pages
File Size : 48,6 Mb
Release : 1999
Category : Exponential sums
ISBN : OCLC:271786114

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Character Sums with Exponential Functions and Their Applications by KonUL. Pdf

Author : M. N. Huxley
Publisher : Clarendon Press
Page : 510 pages
File Size : 49,6 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 : M. Jutila
Publisher : Unknown
Page : 134 pages
File Size : 45,8 Mb
Release : 1987
Category : Electronic
ISBN : 8185015996

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

Author : George Richard Herbert Greaves
Publisher : Unknown
Page : 358 pages
File Size : 55,8 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362547

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Sieve Methods, Exponential Sums, and Their Applications in Number Theory by George Richard Herbert Greaves Pdf

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

Author : Matti Jutila
Publisher : Springer Verlag
Page : 0 pages
File Size : 41,5 Mb
Release : 1987
Category : Mathematics
ISBN : 0387183663

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

Author : Yves Chauvin,David E. Rumelhart
Publisher : Psychology Press
Page : 576 pages
File Size : 42,7 Mb
Release : 2013-02-01
Category : Psychology
ISBN : 9781134775811

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Backpropagation by Yves Chauvin,David E. Rumelhart Pdf

Composed of three sections, this book presents the most popular training algorithm for neural networks: backpropagation. The first section presents the theory and principles behind backpropagation as seen from different perspectives such as statistics, machine learning, and dynamical systems. The second presents a number of network architectures that may be designed to match the general concepts of Parallel Distributed Processing with backpropagation learning. Finally, the third section shows how these principles can be applied to a number of different fields related to the cognitive sciences, including control, speech recognition, robotics, image processing, and cognitive psychology. The volume is designed to provide both a solid theoretical foundation and a set of examples that show the versatility of the concepts. Useful to experts in the field, it should also be most helpful to students seeking to understand the basic principles of connectionist learning and to engineers wanting to add neural networks in general -- and backpropagation in particular -- to their set of problem-solving methods.

Author : Konrad Schmüdgen
Publisher : Springer
Page : 512 pages
File Size : 55,7 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9783319645469

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The Moment Problem by Konrad Schmüdgen Pdf

This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.

Author : Louis H.Y. Chen,Larry Goldstein,Qi-Man Shao
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 46,5 Mb
Release : 2010-10-13
Category : Mathematics
ISBN : 9783642150074

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Normal Approximation by Stein’s Method by Louis H.Y. Chen,Larry Goldstein,Qi-Man Shao Pdf

Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.

Author : Anonim
Publisher : Unknown
Page : 1114 pages
File Size : 48,8 Mb
Release : 1991
Category : Physics
ISBN : UOM:39015015962817

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Physics Briefs by Anonim Pdf

Author : National Research Council,Board on Mathematical Sciences and Their Applications,Mathematical Sciences Education Board
Publisher : National Academies Press
Page : 128 pages
File Size : 46,8 Mb
Release : 1989-01-01
Category : Education
ISBN : 9780309185523

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Everybody Counts by National Research Council,Board on Mathematical Sciences and Their Applications,Mathematical Sciences Education Board Pdf

Mathematics is the key to opportunity. No longer only the language of science, mathematics is now essential to business, finance, health, and defense. Yet because of the lack of mathematical literacy, many students are not prepared for tomorrow's jobs. Everybody Counts suggests solutions. Written for everyone concerned about our children's education, this book discusses why students in this country do not perform well in mathematics and outlines a comprehensive plan for revitalizing mathematics education in America, from kindergarten through college. single copy, $8.95; 2-9 copies, $7.50 each; 10 or more copies, $6.95 each (no other discounts apply)