On a senary quartic form

TL;DR

This paper investigates the distribution of rational points of bounded height on a specific senary quartic hypersurface, contributing to the understanding of Manin's conjecture in this context.

Contribution

It provides a count of rational points on a non-normal senary quartic hypersurface, advancing the knowledge of rational point distribution on such varieties.

Findings

Count of rational points aligns with Manin's conjecture predictions

Establishes new techniques for counting points on non-normal hypersurfaces

Provides explicit asymptotic formulas for the number of points

Abstract

We count rational points of bounded height on the non-normal senary quartic hypersurface x 4 = (y 2 1 + $\times$ $\times$ $\times$ + y 2 4)z 2 in the spirit of Manin's conjecture.