Mean value one of prime-pair constants

Details Mean value one of prime-pair constants Mean value one of prime-pair constants

2008-06-10

arxiv.org/abs/0806.1667v1

Mathematics

Number Theory

19 pages, 1 eps figure, 4 tables

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Mean value one of prime-pair constants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mean value one of prime-pair constants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mean value one of prime-pair constants will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-175116