On indefinite integral ternary quadratic forms

Abstract

We resolve two problems pertaining to indefinite integral ternary quadratic forms, one highlighted by Margulis and the other initiated by Serre, both from 1990. To do so we develop tools for dealing with high ramification in problems involving sums over classes of such forms weighted by their diophantine invariants.

Introduction edited, typos corrected, table of notation in Appendix added, other minor edits