Local Fourier uniformity of higher divisor functions on average

2024/02/28 by Mengdi Wang, Wang, Mengdi
Mathematics · #Advanced Harmonic Analysis Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2402.18342

openalex publication_date 2024/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let τ_k be the k-fold divisor function. By constructing an approximant of τ_k, denoted as τ_k^*, which is a normalized truncation of the k-fold divisor function, we prove that when exp(Clog^1/2X(loglog X)^1/2)≤ H≤ X and C>0 is sufficiently large, the following estimate holds for almost all x∈[X,2X]: \[ |∑_x

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