Mean values of arithmetic functions and application to sums of powers

2024/03/28 by Régis de la Bretèche, Gérald Tenenbaum, de la Bretèche, Régis +1
Mathematics · #11N25 #11N64 #11P05 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #secondary 11N37

paper · pdf · doi:10.48550/arxiv.2403.19320

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We provide new upper bounds for sums of certain arithmetic functions in many variables at polynomial arguments and, exploiting recent progress on the mean-value of the Erd\H os-Hooley Δ-function, we derive lower bounds for the cardinality of those integers not exceeding a given limit that are expressible as some sums of powers.

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