Mean value one of prime-pair constants
| dc.creator | van de Bult, Fokko | |
| dc.creator | Korevaar, Jaap | |
| dc.date | 2008-06-10 | |
| dc.date.accessioned | 2026-07-07T09:43:36Z | |
| dc.date.available | 2026-07-07T09:43:36Z | |
| dc.description | For k greater than 1 and r different from 0, let pi^k_{2r}(x) denote the number of prime pairs (p,p^k+2r) with p not exceeding (large) x. By the Bateman-Horn conjecture, the function pi^k_{2r}(x) should be asymptotic to (2/k)C^k_{2r}li_2(x), with certain specific constants C^k_{2r}. Heuristic arguments lead to the conjecture that these constants have mean value one, just like the Hardy-Littlewood constants C_{2r} for prime pairs (p,p+2r). The conjecture is supported by extensive numerical work. | |
| dc.description | 19 pages, 1 eps figure, 4 tables | |
| dc.identifier | https://arxiv.org/abs/0806.1667 | |
| dc.identifier | http://arxiv.org/abs/0806.1667 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162622 | |
| dc.subject | Number Theory | |
| dc.subject | 11P32 | |
| dc.title | Mean value one of prime-pair constants | |
| dc.type | text |