# An instance where the major and minor arc integrals meet

## TL;DR

This paper uses the circle method to derive an asymptotic count of integral points on a specific cubic hypersurface, highlighting a unique case where major and minor arc integrals are both positive and comparable.

## Contribution

It demonstrates a novel application of the circle method where major and minor arc integrals are both positive and of similar size, which is uncommon.

## Key findings

- Asymptotic formula for integral points on a sliced cubic hypersurface
- Major and minor arc integrals are both positive and of the same order
- Highlights a unique case in circle method applications

## Abstract

We apply the circle method to obtain an asymptotic formula for the number of integral points on a certain sliced cubic hypersurface related to the Segre cubic. Unusually, the major and minor arc integrals in this application are both positive and of the same order of magnitude.