Reflection Theorems of Ohno-Nakagawa Type for Quartic Rings and Pairs of $n$-Ary Quadratic Forms

Evan M. O'Dorney, Carnegie Mellon University, Pittsburgh, Pennsylvania.

Chapters 1. Introduction 2. Global-to-local reduction 3. Tame quartic rings with not totally split resolvent, by multijection 4. $2 \times n \times n$ boxes 5. Introduction to counting quartic rings 6. The conic over $ \mathcal {O}_K $ 7. Boxgroups 8. Ring volumes for $\xi '_1$ 9. Ring volumes for $\xi '_2$ 10. Further remarks on the code A. Examples of zone totals