arXiv 1509.043312015-09-14math.NT

General divisor function inequalities and the third cumulant

Zarathustra Brady

发表信息：: Mathematical Proceedings of the Cambridge Philosophical Society, 163(3), 547-560 (2017)
DOI：: 10.1017/S0305004117000147

英文摘要：

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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