The Goldbach conjecture resulting from global-local cuspidal representations and deformations of Galois representations

TL;DR

This paper connects the Langlands program, Galois representation deformations, and quantum deformations to provide a novel approach to the Goldbach conjecture, linking deep number theory concepts with quantum deformation theory.

Contribution

It introduces a new framework using global-local cuspidal representations and quantum deformations of Galois representations to approach the Goldbach conjecture.

Findings

Inverse quantum deformation leads to Goldbach conjecture

Global and local bilinear deformations preserve residue fields

Deformations induce invariance of inertia subgroup orders

Abstract

In the basic general frame of the Langlands global program, a local p-adic elliptic semimodule corresponding to a local (left) cuspidal form is constructed from its global equivalent covered by p-th roots. In the same context, global and local bilinear deformations of Galois representations inducing the invariance of their respective residue fields are introduced as well as global and local bilinear quantum deformations leaving invariant the orders of the inertia subgroups. More particularly, the inverse quantum deformation of a closed curve responsible for its splitting directly leads to the Goldbach conjecture.