The distribution of integers with at least two divisors in a short interval

Details The distribution of integers with at least two divisors in a short interval The distribution of integers with at least two divisors in a short interval

2006-07-19

arxiv.org/abs/math/0607460v3

Quart. J. Math. Oxford 58 (2007), 187-201

Mathematics

Number Theory

12 pages; minor corrections; added abstract and affiliation information

Scientific paper

Let H(x,y,z) be the number of integers $\le x$ with a divisor in (y,z] and let H_1(x,y,z) be the number of integers $\le x$ with exactly one such divisor. When y and z are close, it is expected that H_1(x,y,z) H(x,y,z), that is, an integer with a divisor in (y,z] usually has just one. We determine necessary and sufficient conditions on y and z so that H_1(x,y,z) H(x,y,z). In doing so, we answer an open question from the paper "The distribution of integers with a divisor in a given interval", math.NT/0401223.

Affiliated with

Also associated with

No associations

Rating

The distribution of integers with at least two divisors in a short interval 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 The distribution of integers with at least two divisors in a short interval, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The distribution of integers with at least two divisors in a short interval will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-625828