Vinogradov's theorem with almost equal summands

TL;DR

The paper proves that large odd integers can be expressed as sums of three primes that are nearly equal, with each prime close to one-third of the integer, for heta > 11/20.

Contribution

It establishes a new result on representing large odd integers as sums of three nearly equal primes with a specific bound on their deviation.

Findings

Every large odd integer can be expressed as a sum of three primes within n^{ heta} of n/3 for heta > 11/20.

The result improves understanding of prime partitions with nearly equal summands.

The proof extends previous work on Vinogradov's theorem with additional constraints.

Abstract

Let $\theta > 11/20$. We prove that every sufficiently large odd integer $n$ can be written as a sum of three primes $n = p_1 + p_2 + p_3$ with $|p_i - n/3| \leq n^{\theta}$ for $i\in\{1,2,3\}$.