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

作者：Brady Zarathustra^*

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2017, 163(3): 547-560.

DOI：10.1017/S0305004117000147

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.

• 出版日期2017-11