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The Large Sieve And Its Applications
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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 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 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 realisation 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 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 386 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 On Some Applications of the Large Sieve by : Seppo Pajunen
Download or read book On Some Applications of the Large Sieve written by Seppo Pajunen and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in Multiplicative Number Theory by : Hugh L. Montgomery
Download or read book Topics in Multiplicative Number Theory written by Hugh L. Montgomery and published by Springer. This book was released on 2006-11-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 The Development of the Number Field Sieve by : Arjen K. Lenstra
Download or read book The Development of the Number Field Sieve written by Arjen K. Lenstra and published by Springer. This book was released on 2006-11-15 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
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 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 Algebraic Geometry And Its Applications: Dedicated To Gilles Lachaud On His 60th Birthday - Proceedings Of The First Saga Conference by : Robert Rolland
Download or read book Algebraic Geometry And Its Applications: Dedicated To Gilles Lachaud On His 60th Birthday - Proceedings Of The First Saga Conference written by Robert Rolland and published by World Scientific. This book was released on 2008-04-17 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
Book Synopsis The Large Sieve by : Klaus Friedrich Roth
Download or read book The Large Sieve written by Klaus Friedrich Roth and published by . This book was released on 1969 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 The Large Sieve and Galois Representations by : David James Zywina
Download or read book The Large Sieve and Galois Representations written by David James Zywina and published by . This book was released on 2008 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Number Theory and Its Applications in China by : Yuan Wang
Download or read book Number Theory and Its Applications in China written by Yuan Wang and published by American Mathematical Soc.. This book was released on 1988 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the accomplishments of Chinese number theorists during 1949-1979, a period when correspondence between China and other countries was discouraged. This work presents a survey of the significant contributions of Chinese mathematicians. It also reflects the developments and state of research in number theory in China.