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Author : M. Jutila
Publisher : Unknown
Page : 134 pages
File Size : 43,5 Mb
Release : 1987
Category : Electronic
ISBN : 8185015996
Author : Matti I. Jutila
Publisher : Springer
Page : 138 pages
File Size : 55,9 Mb
Release : 1988-02-19
Category : Mathematics
ISBN : 3540183663
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 : Matti Jutila
Publisher : Springer Verlag
Page : 0 pages
File Size : 47,8 Mb
Release : 1987
Category : Mathematics
ISBN : 0387183663
Author : S. W. Graham,G. Kolesnik
Publisher : Cambridge University Press
Page : 133 pages
File Size : 50,9 Mb
Release : 1991-01-25
Category : Mathematics
ISBN : 9780521339278
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 : G. R. H. Greaves,G. Harman,M. N. Huxley
Publisher : Cambridge University Press
Page : 360 pages
File Size : 50,5 Mb
Release : 1997-01-30
Category : Mathematics
ISBN : 9780521589574
State-of-the-art analytic number theory proceedings.
Author : M. N. Huxley
Publisher : Clarendon Press
Page : 510 pages
File Size : 53,8 Mb
Release : 1996-06-13
Category : Mathematics
ISBN : 9780191590320
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 : N.M Korobov
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 54,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401580328
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 : Richard Mollin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 676 pages
File Size : 45,9 Mb
Release : 2016-12-19
Category : Mathematics
ISBN : 9783110848632
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author : Bretton Woods Workshop on Multiple Dirichlet Series
Publisher : American Mathematical Soc.
Page : 320 pages
File Size : 54,9 Mb
Release : 2006
Category : Dirichlet series
ISBN : 9780821839638
Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet
Author : Hans P. Schlickewei,Eduard Wirsing
Publisher : Springer
Page : 276 pages
File Size : 45,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540462057
The 15 papers of this selection of contributions to the Journées Arithmétiques 1987 include both survey articles and original research papers and represent a cross-section of topics such as Abelian varieties, algebraic integers, arithmetic algebraic geometry, additive number theory, computational number theory, exponential sums, modular forms, transcendence and Diophantine approximation, uniform distribution.
Author : E. Laurincikas,E. Manstavicius,V. Stakenas
Publisher : Walter de Gruyter
Page : 513 pages
File Size : 49,5 Mb
Release : 2012-02-14
Category : Mathematics
ISBN : 9783110944648
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 564 pages
File Size : 45,9 Mb
Release : 2007-11-23
Category : Mathematics
ISBN : 9780306483738
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.
Author : G. R. H. Greaves,G. Harman,M. N. Huxley
Publisher : Unknown
Page : 360 pages
File Size : 48,6 Mb
Release : 1997
Category : Electronic books
ISBN : 110736745X
State-of-the-art analytic number theory proceedings.
Author : Anonim
Publisher : Unknown
Page : 412 pages
File Size : 40,6 Mb
Release : 1992
Category : Number theory
ISBN : UOM:39015033983670
Author : S. W. Graham,Grigori Kolesnik
Publisher : Unknown
Page : 132 pages
File Size : 48,5 Mb
Release : 1991
Category : Electronic books
ISBN : 1107366291
This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums.
