The Large Sieve And Its Applications
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Author | : E. Kowalski |
Publisher | : Cambridge University Press |
Total Pages | : 316 |
Release | : 2008-05-22 |
Genre | : 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 | : E. Kowalski |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2008-05-22 |
Genre | : Mathematics |
ISBN | : 1139472976 |
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.
Author | : Alina Carmen Cojocaru |
Publisher | : Cambridge University Press |
Total Pages | : 250 |
Release | : 2005-12-08 |
Genre | : 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 |
Total Pages | : 386 |
Release | : 2013-09-26 |
Genre | : 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 | : Seppo Pajunen |
Publisher | : |
Total Pages | : |
Release | : 1980 |
Genre | : |
ISBN | : 9789517205207 |
Author | : Hugh L. Montgomery |
Publisher | : Springer |
Total Pages | : 187 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 354036935X |
Author | : Yuan Wang |
Publisher | : World Scientific |
Total Pages | : 342 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9812381597 |
This book provides a detailed description of a most important unsolved mathematical problem ? the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920's. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture.
Author | : Richard A. Mollin |
Publisher | : CRC Press |
Total Pages | : 440 |
Release | : 2009-08-26 |
Genre | : 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 | : Robert Rolland |
Publisher | : World Scientific |
Total Pages | : 530 |
Release | : 2008-04-17 |
Genre | : Mathematics |
ISBN | : 9814471666 |
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.
Author | : H. Davenport |
Publisher | : Springer Science & Business Media |
Total Pages | : 188 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1475759274 |
Although it was in print for a short time only, the original edition of Multiplicative Number Theory had a major impact on research and on young mathematicians. By giving a connected account of the large sieve and Bombieri's theorem, Professor Davenport made accessible an important body of new discoveries. With this stimula tion, such great progress was made that our current understanding of these topics extends well beyond what was known in 1966. As the main results can now be proved much more easily. I made the radical decision to rewrite §§23-29 completely for the second edition. In making these alterations I have tried to preserve the tone and spirit of the original. Rather than derive Bombieri's theorem from a zero density estimate tor L timctions, as Davenport did, I have chosen to present Vaughan'S elementary proof of Bombieri's theorem. This approach depends on Vaughan's simplified version of Vinogradov's method for estimating sums over prime numbers (see §24). Vinogradov devised his method in order to estimate the sum LPH e(prx); to maintain the historical perspective I have inserted (in §§25, 26) a discussion of this exponential sum and its application to sums of primes, before turning to the large sieve and Bombieri's theorem. Before Professor Davenport's untimely death in 1969, several mathematicians had suggested small improvements which might be made in Multiplicative Number Theory, should it ever be reprinted.