On Artin's conjecture: linear slices of diagonal hypersurfaces

TL;DR

This paper investigates Artin's conjecture, proving it for forms that are diagonal on hyperplanes, thus extending the understanding of when the conjecture holds.

Contribution

The paper provides a proof of Artin's conjecture for a new class of forms, specifically those diagonal on hyperplanes, which was previously unresolved.

Findings

Artin's conjecture holds for diagonal forms on hyperplanes

Extension of the conjecture's validity to new form classes

Enhanced understanding of diagonal hypersurfaces

Abstract

Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.