Asymptotically exact heuristics for prime divisors of a^k+b^k

Details Asymptotically exact heuristics for prime divisors of a^k+b^k Asymptotically exact heuristics for prime divisors of a^k+b^k

2003-11-26

arxiv.org/abs/math/0311483v1

J. Integer Seq. 9 (2006), Article 06.2.8

Mathematics

Number Theory

11 pages, 1 table

Scientific paper

Let N_{a,b}(x) count the number of primes p<=x with p dividing a^k+b^k for some k>=1. It is known that asymptotically N_{a,b}(x) grows like c(a,b)x/log x for some rational number c(a,b) that depends in a rather intricate way on a and b. A simple heuristic formula for N_{a,b}(x) is proposed and it is proved that it is asymptotically exact, i.e. has the same asymptotic behaviour as N_{a,b}(x). Connections with Ramanujan sums and character sums are discussed.

Affiliated with

Also associated with

No associations

Rating

Asymptotically exact heuristics for prime divisors of a^k+b^k 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 Asymptotically exact heuristics for prime divisors of a^k+b^k, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotically exact heuristics for prime divisors of a^k+b^k will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-122594