On the Representation of Integers by the Lorentzian Quadratic Form

In this paper, we establish an asymptotic formula, for large radiusr, for the number of representations of a nonzero integerkby the Lorentzian quadratic formx21+x22+…+x2n−x2n+1that are contained in the ball of radiusrcentered at the origin in Euclidean (n+1)-space.