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

Author:

BRADY ZARATHUSTRA

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference11 articles.

1. A New Proof of a Theorem of Van Der Corput

2. A. Pokrovskiy . A linear bound on the Manickam–Miklos–Singhi Conjecture. ArXiv e-prints (Aug. 2013).

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5. FEDJA (http://mathoverflow.net/users/1131/fedja). lower-bound for Pr[X ≥ EX]. MathOverflow. URL:http://mathoverflow.net/q/188087 (version: 2014-11-26).

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