The Large Sieve and Its Applications
Arithmetic Geometry, Random Walks and Discrete Groups
By (author) Emmanuel Kowalski
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Large Sieve and Its Applications by Emmanuel Kowalski
Book DescriptionAmong 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.
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Book DetailsISBN: 9780521888516
(228mm x 152mm x 23mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 22-May-2008
Country of Publication: United Kingdom
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Author Biography - Emmanuel Kowalski
Emmanuel Kowalski is Professor in the Departement Mathematik at ETH Zurich.
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