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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 19. Issue 1 & 2


Published on

December, 2024


Pages

87-96


DOI

https://doi.org/10.2478/udt-2024-0007

Article

Sumsets with Prescribed Lower and Upper Asymptotic Densities II


Authors

Georges Grekos, Ram Krishna Pandey and Sai Teja Somu


Abstract

We show that for natural numbers h, k, such that k ≥ 2, and for real numbers α1, α2, such that 0 <α1 ≤ α2 < 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 α1 and α2, respectively.


Citation

Grekos, G., Pandey, R.K. & Somu, S.T. (2024). Sumsets with Prescribed Lower and Upper Asymptotic Densities II. Uniform distribution theory, 19(1-2), 87-96. https://doi.org/10.2478/udt-2024-0007