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On a problem of Nathanson related to strongly minimal asymptotic bases of order $h$

Year: 2026

Type: preprint

Abstract: Let $h\geq2$ be an integer and let $1/h<θ\leq1/(h-1)$. In this paper, we prove that there exists a strongly minimal asymptotic basis $A$ of order $h$ such that $A(x)\asymp x^θ$. This solves a problem posed by Nathanson in 1988.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.38865

Author: Chen, Shi-Qiang

Institution: Anhui Normal University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Anhui Province, University Natural Science Research Project of Anhui Province

Awards: G5069114726, G7619850904, G8892274570

OpenAlex ID: W7215106193

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