Least zero of a cubic form

TL;DR

This paper establishes an effective bound for finding the smallest non-trivial integer zero of any integral cubic form with at least 17 variables, advancing understanding of solutions to cubic equations.

Contribution

It provides a new effective search bound for the least zero of cubic forms in 17 or more variables, improving previous theoretical results.

Findings

Established an explicit search bound for cubic forms

Applied the bound to find small integer zeros

Enhanced methods for solving cubic equations

Abstract

An effective search bound is established for the least non-trivial integer zero of an arbitrary integral cubic form in at least 17 variables.