Quantitative Oppenheim Conjecture for Quadratic Forms in 5 Variables over Function Fields

TL;DR

This paper extends the quantitative Oppenheim conjecture for indefinite quadratic forms in five variables to the setting of function fields, translating classical results into a new algebraic context.

Contribution

It adapts Davenport's and Heilbronn's methods to function fields, providing a new perspective on quadratic forms in this setting.

Findings

Established a quantitative version of the Oppenheim conjecture over function fields.

Translated classical results from number fields to function fields.

Provided new tools for analyzing quadratic forms in algebraic function field contexts.

Abstract

We translate Davenport's and Heilbronn's work on a quantitative version of the Oppenheim conjecture for indefinite diagonal quadratic forms in 5 variables into the setting of function fields.