
TL;DR
This paper investigates solutions to certain homogeneous Diophantine equations, providing simplifications of previous results and heuristics for related conjectures, with implications for Thue equations and lattice theory.
Contribution
It offers simplified proofs of Stewart's results and develops heuristics for conjectures related to Thue equations involving lattices.
Findings
Simplified Stewart's results on Thue equations
Developed heuristics for Stewart's conjecture
Provided new insights into Diophantine equations with lattice structures
Abstract
We consider Diophantine equations of the kind , where is a homogeneous polynomial of degree that has non-zero discriminant and is a positive integer. We prove results that simplify those of Stewart and provide heuristics for a conjecture of Stewart.
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