Sumsets with Prescribed Lower and Upper Asymptotic Densities II
Abstract We show that for natural numbers h, k, such that k ≥ 2, and for real numbers α 1 , α 2 , such that 0 <α 1 ≤ α 2 < 1, there exists a subset A of ℕ = {0, 1, 2,... }, such that for all finite subsets B of ℕ such that max B − min B = h, the lower and upper asymptotic densities of kA + B are α 1 and α 2 , respectively.
Authors
- Ram Krishna Pandey (ORCID: https://orcid.org/0000-0002-5791-6007)
- Georges Grekos
- Sai Teja Somu (ORCID: https://orcid.org/0000-0002-3240-8380)
Institutions
- Indian Institute of Technology Roorkee (IN)
- Institut Camille Jordan (FR)
- Université Jean Monnet (FR)
Publication Details
- Journal
- Uniform distribution theory
- Published
- 2024-12-01
- DOI
- https://doi.org/10.2478/udt-2024-0007
- Primary Topic
- Approximation Theory and Sequence Spaces
- Type
- article
- Field-Weighted Citation Impact
- 0.00