Improved Average Bounds for an Inequality of Alladi, Erdös, and Vaaler

2025/09/16 by Cooper O'Kuhn, O'Kuhn, Cooper
Mathematics · #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2509.12570

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We prove an averaged version of a claim suspected to be true by Alladi, Erdös, 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.

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