On The Local Sum Conjecture in Two Dimensions

TL;DR

This paper provides an accessible, elementary proof of the local sum conjecture in two dimensions, simplifying previous complex methods that combined algebraic geometry and logic.

Contribution

It offers a new, simplified proof of the two-dimensional case, making the result more accessible to a broader mathematical audience.

Findings

Elementary proof of the local sum conjecture in two dimensions

Simplification of previous complex techniques

Broader accessibility for mathematicians

Abstract

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a research area blending algebraic geometry with ideas from logic. The purpose of this paper is to give an elementary proof of this conjecture which will be accessbile to a broad readership.