English

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.

Keywords

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!