Pairs of diagonal quartic forms: the non-singular Hasse principle

TL;DR

This paper proves that pairs of non-singular diagonal quartic equations in at least 22 variables satisfy the Hasse principle, confirming the existence of rational solutions under certain conditions.

Contribution

It establishes the non-singular Hasse principle for pairs of diagonal quartic forms in 22 or more variables, advancing understanding of rational solutions for such equations.

Findings

Hasse principle holds for pairs of diagonal quartic forms in ≥22 variables

Rational solutions exist under non-singularity conditions

Extends previous results to higher variable counts

Abstract

We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in $22$ or more variables.