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On gaps between squarefree numbers. (English) Zbl 0723.11044

Analytic number theory, Proc. Conf. in Honor of Paul T. Bateman, Urbana/IL (USA) 1989, Prog. Math. 85, 235-253 (1990).
[For the entire collection see Zbl 0711.00008.]
This is a further improvement of the method of finding a small number \(h=h(x)\) such that the interval \((x,x+h)\) contains a squarefree integer. The authors prove that \(h=cx^{3/14}\) is admissible.
One can hope to improve their result by using a better estimate of the related exponential sums (probably, the Iwaniec-Mozzochi method will work the best).

MSC:

11N25 Distribution of integers with specified multiplicative constraints
11B05 Density, gaps, topology

Citations:

Zbl 0711.00008