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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The number of factorizations of numbers less than $x$ into factors less than $y$

Author: Douglas Hensley
Journal: Trans. Amer. Math. Soc. 275 (1983), 477-496
MSC: Primary 10H25; Secondary 10K20, 60F10
MathSciNet review: 682714
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Abstract: Let $K(x,y)$ be the number in the title. There is a function $f(r)$, concave and decreasing with $f(0) = 2$ and $f’(0) = 0$ such that if $r = \sqrt {\log x} /\log y$ then as $x \to \infty$ with $r$ fixed, \[ K(x,y) = x \exp \left ({f(r) \sqrt {\log x} + O {{(\log \log x)}^2}} \right )\]. The proof uses a uniform version of Chernoff’s theorem on large deviations from the sample mean of a sum of $N$ independent random variables.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1983 American Mathematical Society