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Author : G. R. H. Greaves,G. Harman,M. N. Huxley
Publisher : Cambridge University Press
Page : 360 pages
File Size : 48,7 Mb
Release : 1997-01-30
Category : Mathematics
ISBN : 9780521589574
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 : 42,5 Mb
Release : 1997
Category : Electronic books
ISBN : 110736745X
State-of-the-art analytic number theory proceedings.
Author : George Richard Herbert Greaves
Publisher : Unknown
Page : 358 pages
File Size : 52,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362547
State-of-the-art analytic number theory proceedings.
Author : N.M Korobov
Publisher : Springer Science & Business Media
Page : 223 pages
File Size : 51,7 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 : Glyn Harman
Publisher : Princeton University Press
Page : 378 pages
File Size : 53,7 Mb
Release : 2020-05-26
Category : Mathematics
ISBN : 9780691202990
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.
Author : Harold G. Diamond,H. Halberstam,William F. Galway
Publisher : Cambridge University Press
Page : 266 pages
File Size : 49,8 Mb
Release : 2008-10-16
Category : Mathematics
ISBN : 9781139474917
Nearly a hundred years have passed since Viggo Brun invented his famous sieve, and the use of sieve methods is constantly evolving. As probability and combinatorics have penetrated the fabric of mathematical activity, sieve methods have become more versatile and sophisticated and in recent years have played a part in some of the most spectacular mathematical discoveries. Many arithmetical investigations encounter a combinatorial problem that requires a sieving argument, and this tract offers a modern and reliable guide in such situations. The theory of higher dimensional sieves is thoroughly explored, and examples are provided throughout. A Mathematica® software package for sieve-theoretical calculations is provided on the authors' website. To further benefit readers, the Appendix describes methods for computing sieve functions. These methods are generally applicable to the computation of other functions used in analytic number theory. The appendix also illustrates features of Mathematica® which aid in the computation of such functions.
Author : Alina Carmen Cojocaru,M. Ram Murty
Publisher : Cambridge University Press
Page : 250 pages
File Size : 47,5 Mb
Release : 2005-12-08
Category : Mathematics
ISBN : 0521848164
Rather than focus on the technical details which can obscure the beauty of sieve theory, the authors focus on examples and applications, developing the theory in parallel.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,7 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9789814474870
Author : George Greaves
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 51,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662046586
This book surveys the current state of the "small" sieve methods developed by Brun, Selberg and later workers. The book is suitable for university graduates making their first acquaintance with the subject, leading them towards the frontiers of modern research and unsolved problems in the subject area.
Author : R.P. Bambah,V.C. Dumir,R.J. Hans-Gill
Publisher : Birkhäuser
Page : 525 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034870238
The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.
Author : Matti I. Jutila
Publisher : Springer
Page : 138 pages
File Size : 40,5 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 : Yoichi Motohashi
Publisher : Cambridge University Press
Page : 396 pages
File Size : 46,8 Mb
Release : 1997-10-16
Category : Mathematics
ISBN : 9780521625128
Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.
Author : Bruce Berndt,M.A. Bennett,N. Boston,H.G. Diamond,A.J. Hildebrand,W. Philipp
Publisher : CRC Press
Page : 368 pages
File Size : 46,8 Mb
Release : 2002-11-20
Category : Mathematics
ISBN : 9781000065282
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.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 44,6 Mb
Release : 2024-06-17
Category : Electronic
ISBN : 9789814466240
Author : Shigeru Kanemitsu,Hongze Li,Jianya Liu
Publisher : World Scientific
Page : 272 pages
File Size : 53,6 Mb
Release : 2013-02-20
Category : Mathematics
ISBN : 9789814452465
This volume is based on the successful 6th China–Japan Seminar on number theory that was held in Shanghai Jiao Tong University in August 2011. It is a compilation of survey papers as well as original works by distinguished researchers in their respective fields. The topics range from traditional analytic number theory — additive problems, divisor problems, Diophantine equations — to elliptic curves and automorphic L-functions. It contains new developments in number theory and the topics complement the existing two volumes from the previous seminars which can be found in the same book series. Contents:On Jacobi Forms with Levels (Hiroki Aoki)Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (Jörg Brüdern, Koichi Kawada and Trevor D Wooley)Annexe to the Gallery: An Addendum to “Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review” (Jörg Brüdern, Koichi Kawada and Trevor D Wooley)A Note on the Distribution of Primes in Arithmetic Progressions (Zhen Cui and Boqing Xue)Matrices of Finite Abelian Groups, Finite Fourier Transform and Codes (Shigeru Kanemitsu and Michel Waldschmidt)A Remark on a Result of Eichler (Yoshiyuki Kitaoka)On Weyl Sums over Primes in Short Intervals (Angel V Kumchev)On Congruences for Certain Binomial Coefficients of E Lehmer's Type (Takako Kuzumaki and Jerzy Urbanowicz)Sign Changes of the Coefficients of Automorphic L-Functions (Yuk-Kam Lau, Jianya Liu and Jie Wu)On Fourier Coefficients of Automorphic Forms (Guangshi Lü)The Twists of Hessian Elliptic Curves over Splitting Fields of Cubic Polynomials and the Related Elliptic 3-Folds (Katsuya Miyake)Asymptotic Voronoi's Summation Formulas and Their Duality for SL3(ℤ) (Xiumin Ren and Yangbo Ye)Jerzy Urbanowicz's Work in Pure Mathematics (Andrzej Schinzel)Conjectures Involving Arithmetical Sequences (Zhi-Wei Sun) Readership: Graduate students and researchers in number theory. Keywords:Diophantine Equation;Hessian Elliptic Curves;Automorphic L-functions;Jacobi Forms;Weyl Sums;Fourier Coefficients;Result of Eichler;Distribution of Primes in Arithmetic Progression
