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Solutions to a Romanoff type problem

Yuchen Ding

Abstract

We answer negatively a 2014 problem of Yang and Chen on Romanoff type representations. Sharp results involving their problem were also obtained in this article.

Solutions to a Romanoff type problem

Abstract

We answer negatively a 2014 problem of Yang and Chen on Romanoff type representations. Sharp results involving their problem were also obtained in this article.
Paper Structure (3 sections, 2 theorems, 42 equations)

This paper contains 3 sections, 2 theorems, 42 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['th1']}
  3. Proof of Theorem \ref{['th2']}

Key Result

Theorem 1.1

Let $\alpha>0$ be arbitrarily small given number and $\mathcal{B}$ a subset of $\mathbb{N}$ with $c$-condition such that $\mathcal{B}(x)\gg x^{\alpha}$. Then

Theorems & Definitions (4)

  • Theorem 1.1
  • Theorem 1.2
  • proof : Proof of Theorem \ref{['th1']}
  • proof : Proof of Theorem \ref{['th2']}