Some optimal links between generations of correlation averages

2015/05/18 by Giovanni Coppola, Coppola, Giovanni, Maurizio Laporta +1
Mathematics · #11N37 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11N37

paper · pdf · doi:10.48550/arxiv.1505.04551

5 pages

arxiv created 2015/05/18 · openalex publication_date 2015/05/18 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a real-valued and essentially bounded arithmetic function f, i.e., f(n)≪_ε n^ε, ∀ε > 0, we \enspace give some optimal links between non-trivial bounds for the sums ∑_{h≤ H}∑_{N<n≤ 2N}f(n)f(n-h), ∑_{N<x≤ 2N} | ∑_{x<n≤ x+H}f(n)|² and ∑_{N<n≤ 2N} | ∑_{0≤ |n-x|≤ H}(1-|n-x|\over H)f(n)|², with H=o(N) as N→∞.

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