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

TL;DR

This paper investigates the structure of non-archimedean masses of quadratic lattices over number fields, providing a fundamental structural result and applying it to derive an analytic class number formula for CM extensions.

Contribution

It establishes a fundamental structural theorem for formal series encoding masses of quadratic lattices with fixed rank and signature over number fields, including local computations and class number formulas.

Findings

Structural result for formal series of lattice masses

Local computations for rank 2 lattices

Analytic class number formula for CM extensions

Abstract

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.