Article
Sets With Prescribed Arithmetic Densities
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Abstract
Using concepts of generalized asymptotic and logarithmic densi- ties based on weighted arithmetic means over an arithmetical semigroup G we prove that under some additional technical assumptions on the weighted count- ing function of its elements, a subset of G exists with all four generalized densities (upper and lower asymptotic and logarithmic) prescribed subject to the natural condition 0 ≤ d(A) ≤(A) ≤(A) ≤ d(A) ≤ 1.
Keywords
Generalized arithmetic density, generalized asymptotic density, generalized log arithmic density, arithmetical semigroup, weighted arithmetic mean, ratio set, R-dense set, Axiom A, δ-regularly varying function.
Citation
Luca, F., Pomerance, C., & Porubsky, S. (2008). Sets with prescribed arithmetic densities. Uniform Distribution Theory, 3(2), 67–80.
F. Luca, C. Pomerance and S. Porubsky, “Sets with prescribed arithmetic densities,” Uniform Distribution Theory, vol. 3, no. 2, pp. 67–80, 2008.
Luca F, Pomerance C, Porubsky S. Sets with prescribed arithmetic densities. Uniform Distribution Theory. 2008;3(2):67–80.
Luca, F., Pomerance, C. and Porubsky, S. (2008), ‘Sets with prescribed arithmetic densities’, Uniform Distribution Theory, 3(2), pp. 67–80.
Luca, Florian, et al. “Sets with Prescribed Arithmetic Densities.” Uniform Distribution Theory, vol. 3, no. 2, 2008, pp. 67–80.
Luca, Florian, Carl Pomerance, and Stefan Porubsky. “Sets with Prescribed Arithmetic Densities.” Uniform Distribution Theory 3, no. 2 (2008): 67–80.
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Published by: Engineering Journals
