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PreprintCC BY 4.0arXiv

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

  • Shi-Qiang Chen
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Abstract

Let h≥2 be an integer and let 1/h<θ≤1/(h−1). In this paper, we prove that there exists a strongly minimal asymptotic basis A of order h such that A(x)asymp xθ. This solves a problem posed by Nathanson in 1988.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026problem,
  title = {{On a problem of Nathanson related to strongly minimal asymptotic bases of order $h$}},
  author = {Shi-Qiang Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38865},
  eprint = {2609.38865},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38865},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On a problem of Nathanson related to strongly minimal asymptotic bases of order h
AU  - Shi-Qiang Chen
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.38865
UR  - https://arxiv.org/abs/2609.38865
AB  - Let h≥2 be an integer and let 1/h<θ≤1/(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.
ER  -