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The Sum-of-Digits-Function and Uniform Distribution Modulo 1

✍ Scribed by Michael Drmota; Gerhard Larcher

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
210 KB
Volume
89
Category
Article
ISSN
0022-314X

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✦ Synopsis

The aim of this paper is to provide detailed estimates for the discrepancy of the sequences ([: } s q (n)]) ([x] denotes the fractional part of x) and results concerning the uniform distribution and the discrepancy of the sequences ([: 1 } s q 1 (n)], ..., [: d } s q d (n)]), where :, : 1 , ..., : d are fixed irrational numbers and s q (n) denotes the q-ary sum-of-digits-function.

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