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

Kevin Ford (1) , Gérald Tenenbaum (2)

1 Mathematics
2 IECN - Institut Élie Cartan de Nancy

We determine the true order of magnitude of the number of integers not exceeding x which have a prescribed number of divisors in a short interval, precisely defined in the text.

Mots clés: divisors; sieve

Domaines: Théorie des nombres [math.NT]

Kevin Ford, Gérald Tenenbaum. The distribution of integers with at least two divisors in a short interval. The Quarterly Journal of Mathematics, 2007. ⟨hal-00091331⟩