Integer sequences of the form , where 1 < c < 2, can be locally approximated by sequences of the form ⌊nα+β⌋ in a very good way. Following this approach, we are led to an estimate of the difference , which measures the deviation of the mean value of φ on the subsequence from the expected value, by an expression involving exponential sums. As an application we prove that for 1 < c ≤ 1.42 the subsequence of the Thue-Morse sequence indexed by attains both of its values with asymptotic density 1/2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-3-1,
author = {Lukas Spiegelhofer},
title = {Piatetski-Shapiro sequences via Beatty sequences},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {201-229},
zbl = {06373518},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-3-1}
}
Lukas Spiegelhofer. Piatetski-Shapiro sequences via Beatty sequences. Acta Arithmetica, Tome 166 (2014) pp. 201-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-3-1/