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Divisor function inequalities, entropy, and the chance of being below average

Published online by Cambridge University Press:  01 March 2017

ZARATHUSTRA BRADY
ZARATHUSTRA BRADY*
Affiliation:
Department of Mathematics, Stanford University, 450 Serra Mall, Bldg. 380, Stanford, CA 94305-2125, U.S.A. e-mail: notzeb@stanford.edu
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 3 , November 2017 , pp. 547 - 560
Copyright
Copyright © Cambridge Philosophical Society 2017 

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References

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