Abstract
The main result concerns the distribution of Ω(n) within
There is an average value k0 for Ω(n), and a dispersion parameter V,such that for k not too far from k0, and for large x, y with
the number of solutions n of Ω(n) = k in S(x,y) is roughly exp(-V(k-k0)2) times the number of solutions n of Ω(n) = k0 in S(x,y).
In the course of the proof, machinery is developed which permits a sharpening in the same range of previous estimates for the local behaviour of ψ(x,y) as a function of x.
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References
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© 1987 Birkhäuser Boston
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Hensley, D. (1987). The Distribution of Ω(n) among Numbers with No Large Prime Factors. In: Adolphson, A.C., Conrey, J.B., Ghosh, A., Yager, R.I. (eds) Analytic Number Theory and Diophantine Problems. Progress in Mathematics, vol 70. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4816-3_14
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DOI: https://doi.org/10.1007/978-1-4612-4816-3_14
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