Smooth squarefree and square-full integers in arithmetic progressions
Number Theory
2019-03-11 v2
Abstract
We obtain new lower bounds on the number of smooth squarefree integers up to in residue classes modulo a prime , relatively large compared to , which in some ranges of and improve that of A. Balog and C. Pomerance (1992). We also estimate the smallest squarefull number in almost all residue classes modulo a prime .
Cite
@article{arxiv.1810.02573,
title = {Smooth squarefree and square-full integers in arithmetic progressions},
author = {Marc Munsch and Igor E. Shparlinski and Kam Hung Yau},
journal= {arXiv preprint arXiv:1810.02573},
year = {2019}
}