Unipotent Flows And Isotropic Quadratic Forms In Positive Characteristic

TL;DR

This paper proves an analogue of the Oppenheim conjecture for isotropic quadratic forms over local fields of positive characteristic, using dynamical methods, especially addressing the complex case of characteristic 3.

Contribution

It establishes the positive characteristic analogue of the Oppenheim conjecture, extending the understanding of quadratic forms over local fields.

Findings

Proved the conjecture for all positive characteristic cases.

Developed dynamical techniques for characteristic 3.

Extended the theory of quadratic forms in positive characteristic.

Abstract

The analogous statement to Oppenheim conjecture over a local field of positive characteristic is proved. The dynamical argument is most involved in the case of characteristic 3.