Applications of Sieve Methods to the Theory of Numbers
Author : C. Hooley
Publisher :
Page : 122 pages
File Size : 31,55 MB
Release : 1976
Category : Cribles (Mathématiques)
ISBN :
Author : C. Hooley
Publisher :
Page : 122 pages
File Size : 31,55 MB
Release : 1976
Category : Cribles (Mathématiques)
ISBN :
Author : Alina Carmen Cojocaru
Publisher : Cambridge University Press
Page : 250 pages
File Size : 13,41 MB
Release : 2005-12-08
Category : Mathematics
ISBN : 9780521848169
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 : Heine Halberstam
Publisher : Courier Corporation
Page : 386 pages
File Size : 19,52 MB
Release : 2013-09-26
Category : Mathematics
ISBN : 0486320804
This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition.
Author : C. Hooley
Publisher :
Page : 119 pages
File Size : 33,58 MB
Release : 1976
Category :
ISBN :
Author : G. R. H. Greaves
Publisher : Cambridge University Press
Page : 360 pages
File Size : 44,11 MB
Release : 1997-01-30
Category : Mathematics
ISBN : 0521589576
State-of-the-art analytic number theory proceedings.
Author : Richard A. Mollin
Publisher : CRC Press
Page : 440 pages
File Size : 45,77 MB
Release : 2009-08-26
Category : Computers
ISBN : 1420083295
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and mo
Author : Glyn Harman
Publisher : Princeton University Press
Page : 380 pages
File Size : 49,97 MB
Release : 2012-11-26
Category : Mathematics
ISBN : 1400845939
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 : E. Kowalski
Publisher : Cambridge University Press
Page : 316 pages
File Size : 41,81 MB
Release : 2008-05-22
Category : Mathematics
ISBN : 9780521888516
Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.
Author : John B. Friedlander
Publisher : American Mathematical Soc.
Page : 554 pages
File Size : 42,7 MB
Release : 2010-06-22
Category : Mathematics
ISBN : 0821849700
This is a true masterpiece that will prove to be indispensable to the serious researcher for many years to come. --Enrico Bombieri, Institute for Advanced Study This is a truly comprehensive account of sieves and their applications, by two of the world's greatest authorities. Beginners will find a thorough introduction to the subject, with plenty of helpful motivation. The more practised reader will appreciate the authors' insights into some of the more mysterious parts of the theory, as well as the wealth of new examples. --Roger Heath-Brown, University of Oxford, Fellow of Royal Society This is a comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. Included is a wide range of applications, both to traditional questions such as those concerning primes, and to areas previously unexplored by sieve methods, such as elliptic curves, points on cubic surfaces and quantum ergodicity. New proofs are given also of some of the central theorems of analytic number theory; these proofs emphasize and take advantage of the applicability of sieve ideas. The book contains numerous comments which provide the reader with insight into the workings of the subject, both as to what the sieve can do and what it cannot do. The authors reveal recent developements by which the parity barrier can be breached, exposing golden nuggets of the subject, previously inaccessible. The variety in the topics covered and in the levels of difficulty encountered makes this a work of value to novices and experts alike, both as an educational tool and a basic reference.
Author : G. Tenenbaum
Publisher : Cambridge University Press
Page : 180 pages
File Size : 48,52 MB
Release : 1995-06-30
Category : Mathematics
ISBN : 9780521412612
This is a self-contained introduction to analytic methods in number theory, assuming on the part of the reader only what is typically learned in a standard undergraduate degree course. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians. These aspects are aided by the inclusion at the end of each chapter a section of bibliographic notes and detailed exercises.