Improved Average Bounds for an Inequality of Alladi, Erd\"os, and Vaaler
Number Theory
2025-09-17 v1
Abstract
We prove an averaged version of a claim suspected to be true by Alladi, Erd\"os, and Vaaler. Qualitatively, the result states that a divisor sum of a multiplicative function, which obeys certain size constraints, derives most of its value from its "small" divisors.
Cite
@article{arxiv.2509.12570,
title = {Improved Average Bounds for an Inequality of Alladi, Erd\"os, and Vaaler},
author = {Cooper O'Kuhn},
journal= {arXiv preprint arXiv:2509.12570},
year = {2025}
}
Comments
17 pages. Comments and suggestions are welcome!