Explicit formulas for Masses of Ternary Quadratic Lattices of varying determinant over Number Fields

Abstract

This paper gives explicit formulas for the formal total mass Dirichlet series for integer-valued ternary quadratic lattices of varying determinant and fixed signature over number fields F where p = 2 splits completely. We prove this by using local genus invariants and local mass formulas to compute the local factors of the theory developed in [11]. When the signature is positive definite these formulas be checked against tables of positive definite ternary quadratic forms over Z, and we have written specialized software which checks these results when the Hessian determinant is \leq 2 \times 10^4. This work can also be applied to study the 2-parts of class groups of cubic fields (e.g. see [2]).