Van Der Corput S Method Of Exponential Sums

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Van Der Corput's Method of Exponential Sums

S. W. Graham,G. Kolesnik
Van Der Corput s Method of Exponential Sums Book PDF

Author : S. W. Graham,G. Kolesnik
Publisher : Cambridge University Press
Page : 133 pages
File Size : 47,6 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.

Van Der Corput's Method of Exponential Sums

S. W. Graham,Grigori Kolesnik
Van Der Corput s Method of Exponential Sums Book PDF

Author : S. W. Graham,Grigori Kolesnik
Publisher : Unknown
Page : 132 pages
File Size : 45,9 Mb
Release : 1991
Category : Electronic books
ISBN : 1107366291

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Van Der Corput's Method of Exponential Sums by S. W. Graham,Grigori 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.

Lectures on a Method in the Theory of Exponential Sums

Matti I. Jutila
Lectures on a Method in the Theory of Exponential Sums Book PDF

Author : Matti I. Jutila
Publisher : Springer
Page : 138 pages
File Size : 53,6 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.

Area, Lattice Points, and Exponential Sums

M. N. Huxley
Area Lattice Points and Exponential Sums Book PDF

Author : M. N. Huxley
Publisher : Clarendon Press
Page : 510 pages
File Size : 45,8 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.

Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis

Hugh L. Montgomery
Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis Book PDF

Author : Hugh L. Montgomery
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 40,9 Mb
Release : 1994
Category : Analyse harmonique - Congrès
ISBN : 9780821807378

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Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis by Hugh L. Montgomery Pdf

This volume contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One particularly valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. The book should be a useful resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.

Twentieth Century Harmonic Analysis

J.S. Byrnes
Twentieth Century Harmonic Analysis Book PDF

Author : J.S. Byrnes
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401006620

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Twentieth Century Harmonic Analysis by J.S. Byrnes Pdf

Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated. The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.

Meeting under the Integral Sign?: The Oslo Congress of Mathematicians on the Eve of the Second World War

Christopher D. Hollings,Reinhard Siegmund-Schultze
Meeting under the Integral Sign The Oslo Congress of Mathematicians on the Eve of the Second World War Book PDF

Author : Christopher D. Hollings,Reinhard Siegmund-Schultze
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 54,6 Mb
Release : 2020-04-08
Category : Education
ISBN : 9781470443535

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Meeting under the Integral Sign?: The Oslo Congress of Mathematicians on the Eve of the Second World War by Christopher D. Hollings,Reinhard Siegmund-Schultze Pdf

This book examines the historically unique conditions under which the International Congress of Mathematicians took place in Oslo in 1936. This Congress was the only one on this level to be held during the period of the Nazi regime in Germany (1933–1945) and after the wave of emigrations from it. Relying heavily on unpublished archival sources, the authors consider the different goals of the various participants in the Congress, most notably those of the Norwegian organizers, and the Nazi-led German delegation. They also investigate the reasons for the absence of the proposed Soviet and Italian delegations. In addition, aiming to shed light onto the mathematical dimension of the Congress, the authors provide overviews of the nineteen plenary presentations, as well as their planning and development. Biographical information about each of the plenary speakers rounds off the picture. The Oslo Congress, the first at which Fields Medals were awarded, is used as a lens through which the reader of this book can view the state of the art of mathematics in the mid-1930s.

Sequences, Discrepancies and Applications

Michael Drmota,Robert F. Tichy
Sequences Discrepancies and Applications Book PDF

Author : Michael Drmota,Robert F. Tichy
Publisher : Springer
Page : 517 pages
File Size : 53,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540683339

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Sequences, Discrepancies and Applications by Michael Drmota,Robert F. Tichy Pdf

The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.

Encyclopaedia of Mathematics, Supplement III

Michiel Hazewinkel
Encyclopaedia of Mathematics Supplement III Book PDF

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 43,9 Mb
Release : 2007-11-23
Category : Mathematics
ISBN : 9780306483738

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Encyclopaedia of Mathematics, Supplement III by Michiel Hazewinkel Pdf

This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Lattice Points

Ekkehard Krätzel
Lattice Points Book PDF

Author : Ekkehard Krätzel
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 51,8 Mb
Release : 1989-03-31
Category : Mathematics
ISBN : 9027727333

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Lattice Points by Ekkehard Krätzel Pdf

This book is devoted to a special problem of number theory, that is the estimation of the number of lattice points in large closed domains of ordinary Euclidean spaces. Circle and sphere problems, Dirichlet's divisor problem, the distribution of powerful numbers, and finite Abelian groups are also investigated. The object of this book is to acquaint the reader with the fundamental results and methods, so that follow up with the original papers is possible.

Introduction to Analytic and Probabilistic Number Theory

Gérald Tenenbaum
Introduction to Analytic and Probabilistic Number Theory Book PDF

Author : Gérald Tenenbaum
Publisher : American Mathematical Soc.
Page : 629 pages
File Size : 54,8 Mb
Release : 2015-07-16
Category : Number theory
ISBN : 9780821898543

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Introduction to Analytic and Probabilistic Number Theory by Gérald Tenenbaum Pdf

This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. --Mathematical Reviews

Number Theory

Matti Jutila,Tauno Metsänkylä
Number Theory Book PDF

Author : Matti Jutila,Tauno Metsänkylä
Publisher : Walter de Gruyter
Page : 340 pages
File Size : 40,9 Mb
Release : 2014-01-02
Category : Mathematics
ISBN : 9783110870923

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Number Theory by Matti Jutila,Tauno Metsänkylä Pdf

These Proceedings contain 22 refereed research and survey articles based on lectures given at the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, held in Turku, Finland, from May 31 to June 4, 1999. The subject of the symposium was number theory in a broad sense with an emphasis on recent advances and modern methods. The topics covered in this volume include various questions in elementary number theory, new developments in classical Diophantine problems - in particular of the Fermat and Catalan type, the ABC-conjecture, arithmetic algebraic geometry, elliptic curves, Diophantine approximations, Abelian fields, exponential sums, sieve methods, box splines, the Riemann zeta-function and other Dirichlet series, and the spectral theory of automorphic functions with its arithmetical applications.

Number Theory, Fourier Analysis and Geometric Discrepancy

Giancarlo Travaglini
Number Theory Fourier Analysis and Geometric Discrepancy Book PDF

Author : Giancarlo Travaglini
Publisher : Cambridge University Press
Page : 251 pages
File Size : 43,8 Mb
Release : 2014-06-12
Category : Mathematics
ISBN : 9781107044036

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Number Theory, Fourier Analysis and Geometric Discrepancy by Giancarlo Travaglini Pdf

Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.

Analytic Information Theory

Michael Drmota,Wojciech Szpankowski
Analytic Information Theory Book PDF

Author : Michael Drmota,Wojciech Szpankowski
Publisher : Cambridge University Press
Page : 382 pages
File Size : 52,5 Mb
Release : 2023-09-07
Category : Computers
ISBN : 9781108647984

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Analytic Information Theory by Michael Drmota,Wojciech Szpankowski Pdf

Aimed at graduate students and researchers interested in information theory and the analysis of algorithms, this book explores problems of information and learning theory, demonstrating how to use tools from analytic combinatorics to discover and analyze precise behavior of source codes.

Exponential Sums and their Applications

N.M Korobov
Exponential Sums and their Applications Book PDF

Author : N.M Korobov
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 46,7 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.