The principle of the large sieve
| dc.creator | Kowalski, Emmanuel | |
| dc.date | 2006-09-30 | |
| dc.date | 2006-10-29 | |
| dc.date.accessioned | 2026-07-07T07:28:33Z | |
| dc.date.available | 2026-07-07T07:28:33Z | |
| dc.description | 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. | |
| dc.description | 65 pages; some small corrections, and added application to random walk on mapping class groups (non pseudo-Anosov elements form a transient set), based on work of Maher and Rivin | |
| dc.identifier | https://arxiv.org/abs/math/0610021 | |
| dc.identifier | http://arxiv.org/abs/math/0610021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117769 | |
| dc.subject | Number Theory | |
| dc.subject | Group Theory | |
| dc.subject | Probability | |
| dc.subject | 11N35; 11N36, 11C99, 60G50, 22D10, 14G15, 11B37, 20C33 | |
| dc.title | The principle of the large sieve | |
| dc.type | text |