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Applications Of Sieve Methods To The Theory Of Numbers
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Book Synopsis Applications of Sieve Methods to the Theory of Numbers by : C. Hooley
Download or read book Applications of Sieve Methods to the Theory of Numbers written by C. Hooley and published by . This book was released on 1976 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applications of Sieve Methods to the Theory of Numbers by : C. Hooley
Download or read book Applications of Sieve Methods to the Theory of Numbers written by C. Hooley and published by . This book was released on 1976 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Sieve Methods and Their Applications by : Alina Carmen Cojocaru
Download or read book An Introduction to Sieve Methods and Their Applications written by Alina Carmen Cojocaru and published by Cambridge University Press. This book was released on 2005-12-08 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sieve Methods written by Heine Halberstam and published by Courier Corporation. This book was released on 2013-09-26 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sieve Methods, Exponential Sums, and Their Applications in Number Theory by : G. R. H. Greaves
Download or read book Sieve Methods, Exponential Sums, and Their Applications in Number Theory written by G. R. H. Greaves and published by Cambridge University Press. This book was released on 1997-01-30 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art analytic number theory proceedings.
Book Synopsis Advanced Number Theory with Applications by : Richard A. Mollin
Download or read book Advanced Number Theory with Applications written by Richard A. Mollin and published by CRC Press. This book was released on 2009-08-26 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Prime-Detecting Sieves (LMS-33) by : Glyn Harman
Download or read book Prime-Detecting Sieves (LMS-33) written by Glyn Harman and published by Princeton University Press. This book was released on 2020-05-26 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Large Sieve and its Applications by : E. Kowalski
Download or read book The Large Sieve and its Applications written by E. Kowalski and published by Cambridge University Press. This book was released on 2008-05-22 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Opera de Cribro by : John B. Friedlander
Download or read book Opera de Cribro written by John B. Friedlander and published by American Mathematical Soc.. This book was released on 2010-06-22 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Not Always Buried Deep by : Paul Pollack
Download or read book Not Always Buried Deep written by Paul Pollack and published by American Mathematical Soc.. This book was released on 2009-10-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with minimal mathematical background. Solving such problems sometimes requires difficult and deep methods. But this is not a universal phenomenon; many engaging problems can be successfully attacked with little more than one's mathematical bare hands. In this case one says that the problem can be solved in an elementary way. Such elementary methods and the problems to which they apply are the subject of this book. Not Always Buried Deep is designed to be read and enjoyed by those who wish to explore elementary methods in modern number theory. The heart of the book is a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem. Rather than trying to present a comprehensive treatise, Pollack focuses on topics that are particularly attractive and accessible. Other topics covered include Gauss's theory of cyclotomy and its applications to rational reciprocity laws, Hilbert's solution to Waring's problem, and modern work on perfect numbers. The nature of the material means that little is required in terms of prerequisites: The reader is expected to have prior familiarity with number theory at the level of an undergraduate course and a first course in modern algebra (covering groups, rings, and fields). The exposition is complemented by over 200 exercises and 400 references.
Book Synopsis An Introduction to Sieve Methods and Their Applications by : Alina Carmen Cojocaru
Download or read book An Introduction to Sieve Methods and Their Applications written by Alina Carmen Cojocaru and published by . This book was released on 2012-11-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Rational Number Theory in the 20th Century by : Władysław Narkiewicz
Download or read book Rational Number Theory in the 20th Century written by Władysław Narkiewicz and published by Springer Science & Business Media. This book was released on 2011-09-02 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Book Synopsis Multiplicative Number Theory I by : Hugh L. Montgomery
Download or read book Multiplicative Number Theory I written by Hugh L. Montgomery and published by Cambridge University Press. This book was released on 2007 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Book Synopsis The Distribution of Prime Numbers by : Dimitris Koukoulopoulos
Download or read book The Distribution of Prime Numbers written by Dimitris Koukoulopoulos and published by American Mathematical Soc.. This book was released on 2019-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem. Throughout, the emphasis has been placed on explaining the main ideas rather than the most general results available. As a result, several methods are presented in terms of concrete examples that simplify technical details, and theorems are stated in a form that facilitates the understanding of their proof at the cost of sacrificing some generality. Each chapter concludes with numerous exercises of various levels of difficulty aimed to exemplify the material, as well as to expose the readers to more advanced topics and point them to further reading sources.
Book Synopsis Elementary Number Theory with Applications by : Thomas Koshy
Download or read book Elementary Number Theory with Applications written by Thomas Koshy and published by Elsevier. This book was released on 2007-05-08 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East
Book Synopsis The Development of Prime Number Theory by : Wladyslaw Narkiewicz
Download or read book The Development of Prime Number Theory written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.
Book Synopsis Sieve Methods, Exponential Sums, and Their Applications in Number Theory by : G. R. H. Greaves
Download or read book Sieve Methods, Exponential Sums, and Their Applications in Number Theory written by G. R. H. Greaves and published by . This book was released on 1997 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art analytic number theory proceedings.