Article
On the Law of the Iterated Logarithm for the Discrepancy of Sequences (Ηₖx) With Multidimensional Indices
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Abstract
By a classical result of Weyl (1916), for any increasing sequence (n ) of positive integers, (n x) is uniformly distributed mod 1 for almost all x. k k The precise asymptotics of the discrepancy of this sequence is known only in a few cases, e.g., for n = k (Khintchine (1924)) and for lacunary (n ) (Philipp k k (1975)). In this paper we extend Philipp’s result to lacunary sequences with multidimensional indices.
Keywords
Discrepancy, lacunary series, law of the iterated logarithm.
Citation
Aistleitner, C. (2007). On the law of the iterated logarithm for the discrepancy of sequences (ηₖx) with multidimensional indices. Uniform Distribution Theory, 2(2), 89–104.
C. Aistleitner, “On the law of the iterated logarithm for the discrepancy of sequences (ηₖx) with multidimensional indices,” Uniform Distribution Theory, vol. 2, no. 2, pp. 89–104, 2007.
Aistleitner C. On the law of the iterated logarithm for the discrepancy of sequences (ηₖx) with multidimensional indices. Uniform Distribution Theory. 2007;2(2):89–104.
Aistleitner, C. (2007), ‘On the law of the iterated logarithm for the discrepancy of sequences (ηₖx) with multidimensional indices’, Uniform Distribution Theory, 2(2), pp. 89–104.
Aistleitner, Christoph. “On the Law of the Iterated Logarithm for the Discrepancy of Sequences (Ηₖx) with Multidimensional Indices.” Uniform Distribution Theory, vol. 2, no. 2, 2007, pp. 89–104.
Aistleitner, Christoph. “On the Law of the Iterated Logarithm for the Discrepancy of Sequences (Ηₖx) with Multidimensional Indices.” Uniform Distribution Theory 2, no. 2 (2007): 89–104.
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Published by: Engineering Journals
