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

**Authors:** Jonathan Hanke  
**arXiv:** [1109.1054](https://arxiv.org/abs/1109.1054)  
**Date:** 2011-09-06  
**Summary page:** https://www.summarizepaper.com/en/paper/1109.1054v1/

## Key points

- Jonathan Hanke presents explicit formulas for 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.
- The author uses local genus invariants and local mass formulas to compute the local factors of the theory developed in [11].
- These formulas can be checked against tables of positive definite ternary quadratic forms over Z when the signature is positive definite.
- Specialized software has been written to check these results when the Hessian determinant is less than or equal to 2 x 10^4.
- This work has applications beyond its immediate scope as it can also be used to study the two-parts of class groups of cubic fields (e.g., see [2]).
- This paper provides a valuable contribution to the field by providing explicit formulas that can aid in further research on ternary quadratic lattices and their properties over number fields with certain splitting conditions.

## Summary

In the paper "Explicit formulas for Masses of Ternary Quadratic Lattices of varying determinant over Number Fields," Jonathan Hanke presents 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. The author uses local genus invariants and local mass formulas to compute the local factors of the theory developed in [11]. These formulas can be checked against tables of positive definite ternary quadratic forms over Z when the signature is positive definite. To ensure accuracy, specialized software has been written to check these results when the Hessian determinant is less than or equal to 2 x 10^4. This work has applications beyond its immediate scope as it can also be used to study the two-parts of class groups of cubic fields (e.g., see [2]). This paper provides a valuable contribution to the field by providing explicit formulas that can aid in further research on ternary quadratic lattices and their properties over number fields with certain splitting conditions.