Mean value one of prime-pair constants

dc.creatorvan de Bult, Fokko
dc.creatorKorevaar, Jaap
dc.date2008-06-10
dc.date.accessioned2026-07-07T09:43:36Z
dc.date.available2026-07-07T09:43:36Z
dc.descriptionFor 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.description19 pages, 1 eps figure, 4 tables
dc.identifierhttps://arxiv.org/abs/0806.1667
dc.identifierhttp://arxiv.org/abs/0806.1667
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162622
dc.subjectNumber Theory
dc.subject11P32
dc.titleMean value one of prime-pair constants
dc.typetext

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