  In this paper, we investigate the interplay between positive-definite
integral ternary quadratic forms and class numbers. We generalize a result of
Jones relating the theta function for the genus of a quadratic form to the
Hurwitz class numbers, obtaining an asymptotic formula (with a main term and
error term away from finitely many bad square classes $t_j\mathbb{Z}^2$)
relating the number of lattices points in a quadratic space of a given norm
with a sum of class numbers related to that norm and the squarefree part of the
discriminant of the quadratic form on this lattice.
