The Structure of Masses of rank $n$ Quadratic Lattices of varying determinant over number fields

In this paper we establish a fundamental structural result for formal series encoding the total non-archimedean masses of quadratic lattices of varying determinant squareclasses, but with fixed rank $n$ and signature over any fixed number field. We conclude with some local computations for $n=2$, and use these to derive an analytic class number formula for CM extensions.