Sieve Methods Exponential Sums And Their Applications In Number Theory
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Sieve Methods Exponential Sums And Their Applications In Number Theory
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Author : G. R. H. Greaves
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-30
Sieve Methods Exponential Sums And Their Applications In Number Theory written by G. R. H. Greaves and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-30 with Mathematics categories.
State-of-the-art analytic number theory proceedings.
Sieve Methods Exponential Sums And Their Applications In Number Theory
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Author : G. R. H. Greaves
language : en
Publisher:
Release Date : 1997
Sieve Methods Exponential Sums And Their Applications In Number Theory written by G. R. H. Greaves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Electronic books categories.
State-of-the-art analytic number theory proceedings.
Sieve Methods Exponential Sums And Their Applications In Number Theory
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Author : George Richard Herbert Greaves
language : en
Publisher:
Release Date : 2014-05-14
Sieve Methods Exponential Sums And Their Applications In Number Theory written by George Richard Herbert Greaves and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
State-of-the-art analytic number theory proceedings.
Exponential Sums And Their Applications
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Author : N.M Korobov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Exponential Sums And Their Applications written by N.M Korobov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Prime Detecting Sieves Lms 33
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Author : Glyn Harman
language : en
Publisher: Princeton University Press
Release Date : 2020-05-26
Prime Detecting Sieves Lms 33 written by Glyn Harman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-26 with Mathematics categories.
This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information. No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown's work on primes represented as a cube plus twice a cube. This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.
Van Der Corput S Method Of Exponential Sums
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Author : S. W. Graham
language : en
Publisher: Cambridge University Press
Release Date : 1991-01-25
Van Der Corput S Method Of Exponential Sums written by S. W. Graham and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-01-25 with Mathematics categories.
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.
Lectures On A Method In The Theory Of Exponential Sums
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Author : Matti I. Jutila
language : en
Publisher: Springer
Release Date : 1988-02-19
Lectures On A Method In The Theory Of Exponential Sums written by Matti I. Jutila and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-02-19 with Mathematics categories.
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
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Author : M. N. Huxley
language : en
Publisher: Clarendon Press
Release Date : 1996-06-13
Area Lattice Points And Exponential Sums written by M. N. Huxley and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-13 with Mathematics categories.
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.
Analytic Number Theory
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Author : Yoichi Motohashi
language : en
Publisher: Cambridge University Press
Release Date : 1997-10-16
Analytic Number Theory written by Yoichi Motohashi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-16 with Mathematics categories.
Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.
Surveys In Number Theory
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Author : Bruce Berndt
language : en
Publisher: CRC Press
Release Date : 2002-11-20
Surveys In Number Theory written by Bruce Berndt and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-20 with Mathematics categories.
This volume, based on fourteen papers from the Millennial Conference on Number Theory, represents surveys of topics in number theory and provides an outlook into the future of number theory research. It serves as an inspiration to graduate students and as a reference for research mathematicians.