An Asymptotic Formula for the Number of Smooth Values of a Polynomial

Details An Asymptotic Formula for the Number of Smooth Values of a Polynomial An Asymptotic Formula for the Number of Smooth Values of a Polynomial

1999-09-29

arxiv.org/abs/math/9909180v2

J. Number Theory 93 (2002), no. 2, 108-182.

Mathematics

Number Theory

57 pages. Revised version - an appendix has been added and some other material rewritten slightly

Scientific paper

Although we expect to find many smooth numbers (i.e., numbers with no large prime factors) among the values taken by a polynomial with integer coefficients, it is unclear what the asymptotic number of such smooth values should be; this is in contrast to the related problem of counting the number of prime values of a polynomial, for which Bateman and Horn published a conjectured asymptotic formula that is widely believed to be true. We discuss how to employ the Bateman-Horn conjecture to derive an asymptotic formula for the number of smooth values of a polynomial, with the smoothness parameter in a non-trivial range. This conditional result provides a believable heuristic for the number of smooth integers among all values {F(n)}, and also among the values {F(p)} on prime arguments only.

Affiliated with

Also associated with

No associations

Rating

An Asymptotic Formula for the Number of Smooth Values of a Polynomial 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 An Asymptotic Formula for the Number of Smooth Values of a Polynomial, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Asymptotic Formula for the Number of Smooth Values of a Polynomial will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-548543