# Free rational points on smooth hypersurfaces

## TL;DR

This paper uses the Hardy-Littlewood circle method to count rational points of bounded height on smooth hypersurfaces, addressing a question posed by Peyre and focusing on low-degree cases.

## Contribution

It introduces a novel application of the circle method to count 'sufficiently free' rational points on smooth hypersurfaces over the rationals.

## Key findings

- Successfully counts rational points on certain hypersurfaces
- Provides new bounds for the number of rational points
- Addresses Peyre's question in specific cases

## Abstract

Motivated by a recent question of Peyre, we apply the Hardy-Littlewood circle method to count "sufficiently free" rational points of bounded height on arbitrary smooth projective hypersurfaces of low degree that are defined over the rational numbers.