Finiteness criteria for the solutions of a sequence of decomposable form inequalities

TL;DR

This paper establishes a finiteness criterion for solutions to a sequence of semi-$q$-decomposable form equations and inequalities, which are factorized into nonconstant homogeneous polynomials with bounded distributive constant.

Contribution

It introduces a new finiteness criterion for solutions of semi-$q$-decomposable form equations and inequalities with specific factorization properties.

Findings

Finiteness criterion for solutions of semi-$q$-decomposable forms

Applicable to equations with bounded distributive constant

Provides conditions ensuring finite solutions

Abstract

In this paper, we give a finiteness criterion for the solutions of the sequence of semi-$q$-decomposable form equations and inequalities, where the semi-$q$-decomposable form is factorized into a family of $q$ nonconstant homogeneous polynomials with the distributive constant not exceeding a certain number.