On the squarefree and squarefull numbers

Abstract

The main purpose of this paper is using the important works of Heath-Brown, Yoichi Motohashi, Masanori Katsurada and Kohji Matsumoto, and the properties of Dirichlet $L$-functions to study the number of squarefree primitive roots, squarefull primitive roots and squarefree quadratic residues modulo a prime $p$, and give three much sharper asymptotic formulae.