On the k-resultant modulus set problem on varieties over finite fields

Abstract

Let [Formula: see text] be a regular variety, [Formula: see text] be an integer and [Formula: see text]. Covert et al. proved the following generalization of the Erdős–Falconer distance problem that if [Formula: see text], then we have [Formula: see text] In this paper, we provide improvements and extensions of their result.