The Set of Multiples of a Short Interval

R. R. Hall and G. Tenenbaum
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R. R. Hall: York University, Department of Mathematics
G. Tenenbaum: Université de Nancy I, Départment of Mathématiques

Chapter 6 in Number Theory, 1991, pp 119-128 from Springer

Abstract: Abstract Following recent work [11, 14, 15], we denote by H(x,y, z) the number of integers n not exceeding x and having at least one divisor in the interval (y, z]. Thus if A := (y, z] ∩Z+ and B(A) is the set of multiples of A, then H(x, y, z) is the counting function of B(A). To determine the asymptotic behaviour of this quantity with good precision is a difficult and interesting sieve problem with many applications in number theory — see in particular chap. 2 of [11].

Date: 1991
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DOI: 10.1007/978-1-4757-4158-2_6

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