# Sums of four prime cubes in short intervals

## TL;DR

This paper establishes an improved asymptotic formula for counting integers that can be expressed as the sum of four prime cubes within shorter intervals than previously possible.

## Contribution

It provides a new asymptotic formula for the average number of representations of integers as sums of four prime cubes in shorter intervals.

## Key findings

- Proves an asymptotic formula for sums of four prime cubes
- Improves interval length bounds for such representations
- Enhances understanding of prime cube representations in short intervals

## Abstract

We prove that a suitable asymptotic formula for the average number of representations of integers $n=p_{1}^{3}+p_{2}^{3}+p_{3}^{3}+p_{4}^{3}$, where $p_1,p_2,p_3,p_4$ are prime numbers, holds in intervals shorter than the the ones previously known.