I will describe recent work giving an asymptotic formula for a count of primitive integral zeros of an isotropic ternary quadratic form in an orbit under integral automorphs of the form. The constant in the asymptotic is explicitly computed in terms of local data determined by the orbit. This is compared with the well-known asymptotic for the count of all primitive zeros. Together with an extension of results of Kneser by R. Schulze-Pillot on the classes in a genus of representations, this yields a formula for the number of orbits, summed over a genus of forms, in terms of the number of local orbits. For a certain special class of forms a simple explicit formula is given for this number.
This video is part of the Number Theory Web Seminar series.
