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An extension of the Erdős-Turán additive base conjecture via generalized circles of partition

Theophilus Agama

Abstract

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erdős-Turán additive base conjecture.

An extension of the Erdős-Turán additive base conjecture via generalized circles of partition

Abstract

This paper is an extension program of the notion of circle of partition developed in our first paper \cite{CoP}. As an application we prove the Erdős-Turán additive base conjecture.

Paper Structure

This paper contains 3 sections, 2 theorems, 57 equations.

Table of Contents

  1. Introduction and background
  2. Generalized circles of partition
  3. Axial potential of generalized circles of partition

Key Result

Theorem 2.5

Let $\mathbb{A}\subset \mathbb{M}$ and suppose $\# \left \{\mathbb{L}_{[x],[y]}~ \hat{\in}~ \mathcal{C}(\mathbb{G}^s(n),\mathbb{A}^t,\mathbb{N}^u)\right \}>0$ for all sufficiently large values of $n$. If $\mathbb{M}=\mathbb{G}=\mathbb{N}$ with $u=t$ for $s\neq t$ and $|\mathbb{A}^t\cap \mathbb{N}_n

Theorems & Definitions (13)

  • Conjecture 1.1: Erdős-Turán additive basis conjecture
  • Remark 1.2
  • Example 1.3
  • Definition 2.1
  • Definition 2.2
  • Remark 2.3
  • Definition 2.4
  • Theorem 2.5
  • proof
  • Corollary 2.6: Proof of the Erdős-Turán additive base conjecture
  • ...and 3 more