A short proof of the strong three dimensional Gaussian product inequality

TL;DR

This paper presents a simplified analytical proof of the strong three-dimensional Gaussian product inequality, resolving previously open cases for triples of even positive integers.

Contribution

It provides a new, purely analytical proof that simplifies earlier combinatorial and computer-assisted methods, solving open cases in three dimensions.

Findings

Proves the strong Gaussian product inequality in three dimensions.

Simplifies the proof process compared to previous methods.

Solves open cases for triples of even positive integers.

Abstract

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of any triple of even positive integers which remained open so far.