Variance of Squarefull Numbers in Short Intervals II
Abstract
In this paper, we continue the study on variance of the number of squarefull numbers in short intervals (x,x+2xH+H2] with X≤x≤2X. We obtain the expected asymptotic for this variance over the range Xε≤H≤X0.180688… unconditionally and over the optimal range Xε≤H≤X0.25−ε conditionally on the Lindelöf hypothesis or the Riemann hypothesis.
Fields of Study & Subjects
Meromorphic and Entire Functions
Analytic Number Theory Research
Mathematical functions and polynomials
Publication details
- Journal / source
- The Michigan Mathematical Journal
- Volume
- -1
- Issue
- -1
- Publication date
- 1 January 2026