Poisson statistics via the Chinese remainder theorem
| dc.creator | Granville, A. | |
| dc.creator | Kurlberg, P. | |
| dc.date | 2004-12-07 | |
| dc.date | 2005-02-21 | |
| dc.date.accessioned | 2026-07-07T05:15:01Z | |
| dc.date.available | 2026-07-07T05:15:01Z | |
| dc.description | We consider the distribution of spacings between consecutive elements in subsets of Z/qZ where q is highly composite and the subsets are defined via the Chinese remainder theorem. We give a sufficient criterion for the spacing distribution to be Poissonian as the number of prime factors of q tends to infinity, and as an application we show that the value set of a generic polynomial modulo q have Poisson spacings. We also study the spacings of subsets of Z/q_1q_2Z that are created via the Chinese remainder theorem from subsets of Z/q_1Z and Z/q_2Z (for q_1,q_2 coprime), and give criteria for when the spacings modulo q_1q_2 are Poisson. We also give some examples when the spacings modulo q_1q_2 are not Poisson, even though the spacings modulo q_1 and modulo q_2 are both Poisson. | |
| dc.description | 32 pages. Lemma 15 corrected (for the case k=2.) Added reference | |
| dc.identifier | https://arxiv.org/abs/math/0412135 | |
| dc.identifier | http://arxiv.org/abs/math/0412135 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73505 | |
| dc.subject | Number Theory | |
| dc.subject | 11N69, 11K36, 11K06 | |
| dc.title | Poisson statistics via the Chinese remainder theorem | |
| dc.type | text |