Filaseta, Michael; Trifonov, Ognian 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). Reviewer: G.Kolesnik (Los Angeles) Cited in 1 ReviewCited in 1 Document MSC: 11N25 Distribution of integers with specified multiplicative constraints 11B05 Density, gaps, topology Keywords:squarefree numbers Citations:Zbl 0711.00008 PDFBibTeX XML