Variance of Squarefull Numbers in Short Intervals
Abstract
In this paper, we study the variance of the number of squarefull numbers in short intervals. As a result, we are able to prove that, for any 0 < θ < 1/2, almost all short intervals (x, x + x1/2 + θ] contain about ζ(3/2)2 ζ(3) xθ squarefull numbers.
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