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.

• Chapters1. Introduction2. Global-to-local reduction3. Tame quartic rings with not totally split resolvent, by multijection4. $2 \times n \times n$ boxes5. Introduction to counting quartic rings6. The conic over $ \mathcal {O}_K $7. Boxgroups8. Ring volumes for $\xi ’_1$9. Ring volumes for $\xi ’_2$10. Further remarks on the codeA. Examples of zone totals