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- 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 polymials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the deminators 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 BiographyEmmanuel Kowalski is Professor in the Departement Mathematik at ETH Zurich.
- PrizesShortlisted for Diagram Prize for the Oddest Title of the Year 2008.
- Author(s)Emmanuel Kowalski
- PublisherCambridge University Press
- Date of Publication22/05/2008
- Series TitleCambridge Tracts in Mathematics
- Series Part/Volume NumberNo. 175
- Place of PublicationCambridge
- Country of PublicationUnited Kingdom
- ImprintCambridge University Press
- Content Note10 b/w illus. 9 tables 14 exercises
- Weight630 g
- Width152 mm
- Height228 mm
- Spine23 mm
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