Work

An explicit economical additive basis

Year: 2025

Type: article

Abstract: We present an explicit subset $A\subseteq \mathbb{N} = \{0,1,\ldots \}$ such that $A + A = \mathbb{N}$ and for all $\varepsilon \gt 0$ , \begin{equation*}\lim _{N\to \infty }\frac {\big |\big \{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\in A^2\big \}\big |}{N^{\varepsilon }} = 0.\end{equation*} This answers a question of Erdős.

Source: Combinatorics Probability Computing

DOI: 10.1017/s096354832510014x

Authors: Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney, Dmitrii Zakharov

Institutions: University of Illinois Chicago, Stanford University, Columbia University, Massachusetts Institute of Technology

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: National Science Foundation