Article
Note on the Joint Distribution of the Weighted Sum-of-Digits Function Modulo One in Case of Pairwise Coprime Bases
Authors
Abstract
In this note we respond to the open question of Pillichshammer in [Uniform distribution of sequences connected with the weighted sum-of-digits function, Uniform Distribution Theory 2 (2007), 1–10.] : Under which conditions on the weight sequences is the multi-dimensional weighted sum-of-digits function for given pairwise coprime bases uniformly distributed modulo one? We do not give a complete answer, but we give a sufficient condition on the weight sequences. Furthermore, we prove that almost all kinds of weight sequences produce a uni- formly distributed sequence.
Keywords
uniform distribution, sum-of-digits function, weighted, additive.
Citation
Hofer, R. (2007). Note on the joint distribution of the weighted sum-of-digits function modulo one in case of pairwise coprime bases. Uniform Distribution Theory, 2(2), 35–47.
R. Hofer, “Note on the joint distribution of the weighted sum-of-digits function modulo one in case of pairwise coprime bases,” Uniform Distribution Theory, vol. 2, no. 2, pp. 35–47, 2007.
Hofer R. Note on the joint distribution of the weighted sum-of-digits function modulo one in case of pairwise coprime bases. Uniform Distribution Theory. 2007;2(2):35–47.
Hofer, R. (2007), ‘Note on the joint distribution of the weighted sum-of-digits function modulo one in case of pairwise coprime bases’, Uniform Distribution Theory, 2(2), pp. 35–47.
Hofer, Roswitha. “Note on the Joint Distribution of the Weighted Sum-of-digits Function Modulo One in Case of Pairwise Coprime Bases.” Uniform Distribution Theory, vol. 2, no. 2, 2007, pp. 35–47.
Hofer, Roswitha. “Note on the Joint Distribution of the Weighted Sum-of-digits Function Modulo One in Case of Pairwise Coprime Bases.” Uniform Distribution Theory 2, no. 2 (2007): 35–47.
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Published by: Engineering Journals
