On the discrepancy of some special sequences

Robert F. Tichy; Gerhard Turnwald

doi:10.1016/0022-314X(87)90096-5

On the discrepancy of some special sequences

Robert F. Tichy^*, Gerhard Turnwald

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain estimates for the discrepancy of the sequence (xs^(d)(q;n))_n=0^∞, where s^(d)(q;n) denotes the sum of the dth powers of the q-ary digits of the nonnegative integer n and x is an irrational number of finite approximation type. Furthermore metric results for a similar type of sequences are given.

Original language	English
Pages (from-to)	68-78
Number of pages	11
Journal	Journal of Number Theory
Volume	26
Issue number	1
DOIs	https://doi.org/10.1016/0022-314X(87)90096-5
Publication status	Published - May 1987

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/0022-314X(87)90096-5

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title = "On the discrepancy of some special sequences",

abstract = "We obtain estimates for the discrepancy of the sequence (xs(d)(q;n))n=0∞, where s(d)(q;n) denotes the sum of the dth powers of the q-ary digits of the nonnegative integer n and x is an irrational number of finite approximation type. Furthermore metric results for a similar type of sequences are given.",

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AU - Turnwald, Gerhard

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AB - We obtain estimates for the discrepancy of the sequence (xs(d)(q;n))n=0∞, where s(d)(q;n) denotes the sum of the dth powers of the q-ary digits of the nonnegative integer n and x is an irrational number of finite approximation type. Furthermore metric results for a similar type of sequences are given.

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DO - 10.1016/0022-314X(87)90096-5

M3 - Article

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VL - 26

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JO - Journal of Number Theory

JF - Journal of Number Theory

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On the discrepancy of some special sequences

Abstract

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