Explicit class number formulas for Siegel–Weil averages of ternary quadratic forms

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