Lower bound for the remainder in the prime-pair conjecture
| dc.creator | Korevaar, Jacob | |
| dc.date | 2008-06-25 | |
| dc.date.accessioned | 2026-07-07T09:46:37Z | |
| dc.date.available | 2026-07-07T09:46:37Z | |
| dc.description | For any positive integer r, let pi_{2r}(x) denote the number of prime pairs (p, p+2r) with p not exceeding (large) x. According to the prime-pair conjecture of Hardy and Littlewood, pi_{2r}(x) should be asymptotic to 2C_{2r}li_2(x) with an explicit positive constant C_{2r}. A heuristic argument indicates that the remainder e_{2r}(x) in this approximation cannot be of lower order than x^beta, where beta is the supremum of the real parts of zeta's zeros. The argument also suggests an approximation for pi_{2r}(x) similar to one of Riemann for pi(x). | |
| dc.description | 25 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0806.4057 | |
| dc.identifier | http://arxiv.org/abs/0806.4057 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163591 | |
| dc.subject | Number Theory | |
| dc.subject | 11P32 | |
| dc.title | Lower bound for the remainder in the prime-pair conjecture | |
| dc.type | text |