On the Discrepancy of the $β$-Adic van der Corput Sequence

J. Math. Sci. Univ. Tokyo
Vol. 5 (1998), No. 2, Page 345--366.

Ninomiya, Syoiti
On the Discrepancy of the $β$-Adic van der Corput Sequence
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Abstract:
The $β$-adic \mbox{van der Corput} sequence is constructed. When $β$ satisfies some conditions, the order of discrepancy of the sequence become $O(\log M/M)$ or $O((\log M)^2/M)$.

Keywords: $β$-adic transformation, ergodic theory, low-discrepancy sequence, numerical integration, quasi-Monte Carlo method

Mathematics Subject Classification (1991): 11K36, 11K38, 11K48
Mathematical Reviews Number: MR1633866

Received: 1997-10-29