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Opera de Cribro (Hardcover)
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Opera de Cribro (Hardcover)
Series: Colloquium Publications
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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. No analytic number
theorist should be without this volume, but it will not have a
place on my bookshelves--it will be permanently on my desk! --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 developments 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.
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