Article
Mahler’s Z-Number and 3/2 Number Systems
Authors
Abstract
We improve the results in [1] on the characterization of multiple points in rational based number system, in connection with Mahler’s Z-number problem. As a by-product, we show that when p > q2, there exists a positive x such that the fractional part of x(p/q)n (n = 0, 1, . . . ) stays in a Cantor set (Theorem 2.5). Hausdorff dimension of the set is positive but tends to zero as p → ∞ when q is fixed.
Keywords
Irregularity of distribution, number system, Z-number.
Citation
Akiyama, S. (2008). Mahler’s z-number and 3/2 number systems. Uniform Distribution Theory, 3(2), 91–99.
S. Akiyama, “Mahler’s z-number and 3/2 number systems,” Uniform Distribution Theory, vol. 3, no. 2, pp. 91–99, 2008.
Akiyama S. Mahler’s z-number and 3/2 number systems. Uniform Distribution Theory. 2008;3(2):91–99.
Akiyama, S. (2008), ‘Mahler’s z-number and 3/2 number systems’, Uniform Distribution Theory, 3(2), pp. 91–99.
Akiyama, Shigeki. “Mahler’s Z-number and 3/2 Number Systems.” Uniform Distribution Theory, vol. 3, no. 2, 2008, pp. 91–99.
Akiyama, Shigeki. “Mahler’s Z-number and 3/2 Number Systems.” Uniform Distribution Theory 3, no. 2 (2008): 91–99.
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Published by: Engineering Journals
