General divisor function inequalities and the third cumulant
Number Theory
2018-06-05 v1
Abstract
We extend a lower bound of Munshi on sums over divisors of a number which are less than a fixed power of 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.
Cite
@article{arxiv.1509.04331,
title = {General divisor function inequalities and the third cumulant},
author = {Zarathustra Brady},
journal= {arXiv preprint arXiv:1509.04331},
year = {2018}
}