... while the author enjoyed the hospitality of the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. Finally, the author acknowledges the referee for a thorough reading of the ... ηlog 2.Annals of Mathematics, 168 (2008), 367–433 The distribution of integers with a divisor in a given interval By Kevin FordAbstractWe determine the order of magnitude of H(x, y, z), the number ... that all hypotheses of Lemma 4.9 are satisfied. For each such k we obtain a A 3τ (a) −2W (a; η) a g,αβ(2v log 2)kk!,for some subset A of the squarefree integers a ≤ yα with ω (a) = k andP− (a) ...