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arXiv · 1509.04331

General divisor function inequalities and the third cumulant

Zarathustra Brady
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Abstract

We extend a lower bound of Munshi on sums over divisors of a number $n$ which are less than a fixed power of $n$ from the squarefree case to the general case. In the process we prove a lower bound on the entropy of a geometric distribution with finite support, as well as a lower bound on the probability that a random variable is less than its mean given that it satisfies a natural condition related to its third cumulant.

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Zarathustra Brady. 2015-09-14. General divisor function inequalities and the third cumulant. https://doi.org/10.1017/s0305004117000147

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