Variance of squarefull numbers in short intervals II

2023/11/22 by Tsz Ho Chan, Chan, Tsz Ho
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2311.13463

openalex publication_date 2023/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we continue the study on variance of the number of squarefull numbers in short intervals (x, x + 2 √(x) H + H²] with X ≤ x ≤ 2X. We obtain the expected asymptotic for this variance over the range X^ε≤ H ≤ X^0.180688... unconditionally and over the optimal range X^ε≤ H ≤ X^{0.25 - ε} conditionally on the Riemann Hypothesis or the Lindelöf Hypothesis.

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