Cargando…
The large sieve and its applications : arithmetic geometry, random walks and discrete groups /
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 appl...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
©2008.
|
| Colección: | Cambridge tracts in mathematics ;
175. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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. |
|---|---|
| Descripción Física: | 1 online resource (xxi, 293 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 283-288) and index. |
| ISBN: | 9780521888516 0521888514 9780511400919 0511400918 9780511397295 0511397291 0511398069 9780511398063 9780511542947 0511542941 0511396562 9780511396564 1107187397 9781107187399 1281383848 9781281383846 9786611383848 6611383840 0511398875 9780511398872 |