The principle of the large sieve

Details The principle of the large sieve The principle of the large sieve

2006-09-30

arxiv.org/abs/math/0610021v3

Mathematics

Number Theory

65 pages; some small corrections, and added application to random walk on mapping class groups (non pseudo-Anosov elements for

Scientific paper

We describe a very general abstract form of sieve based on a large sieve inequality which generalizes both the classical sieve inequality of Montgomery (and its higher-dimensional variants), and our recent sieve for Frobenius over function fields. The general framework suggests new applications. We get some first results on the number of prime divisors of ``most'' elements of an elliptic divisibility sequence, and we develop in some detail ``probabilistic'' sieves for random walks on arithmetic groups, e.g., estimating the probability of finding a reducible characteristic polynomial at some step of a random walk on SL(n,Z). In addition to the sieve principle, the applications depend on bounds for a large sieve constant. To prove such bounds involves a variety of deep results, including Property (T) or expanding properties of Cayley graphs, and the Riemann Hypothesis over finite fields. It seems likely that this sieve can have further applications.

Affiliated with

Also associated with

No associations

Rating

The principle of the large sieve does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The principle of the large sieve, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The principle of the large sieve will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-616426