Article
On Weighted Distribution Functions of Sequences
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Abstract
In this paper we prove that the set of logarithmically weighted distribution functions of the sequence of iterated logarithm log(i) n mod 1, n = ni, ni + 1, . . . is the same as the set of classical distribution functions of the sequence log(i−1) n mod 1 for every i = 2, 3, . . . . Also we prove that log(n log n) mod 1 is logarithmically uniformly distributed. This implies that the sequence pn/n mod 1, where pn denotes the nth prime, is also logarithmically uniformly distributed.
Keywords
Distribution function, weights, Helly theorems.
Citation
Antonini, R. G. & Strauch, O. (2008). On weighted distribution functions of sequences. Uniform Distribution Theory, 3(1), 1–18.
R. G. Antonini and O. Strauch, “On weighted distribution functions of sequences,” Uniform Distribution Theory, vol. 3, no. 1, pp. 1–18, 2008.
Antonini RG, Strauch O. On weighted distribution functions of sequences. Uniform Distribution Theory. 2008;3(1):1–18.
Antonini, R. G. and Strauch, O. (2008), ‘On weighted distribution functions of sequences’, Uniform Distribution Theory, 3(1), pp. 1–18.
Antonini, Rita Giuliano, and Oto Strauch. “On Weighted Distribution Functions of Sequences.” Uniform Distribution Theory, vol. 3, no. 1, 2008, pp. 1–18.
Antonini, Rita Giuliano, and Oto Strauch. “On Weighted Distribution Functions of Sequences.” Uniform Distribution Theory 3, no. 1 (2008): 1–18.
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Published by: Engineering Journals
