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- W3086273891 abstract "By using the work of Frantzikinakis and Wierdl, we can see that for all d∈N, α∈(d,d+1), and integers k≥d+2 and r≥1, there exist infinitely many n∈N such that the sequence (⌊(n+rj)α⌋)j=0k−1 is represented as ⌊(n+rj)α⌋=p(j), j=0,1,…,k−1, by using some polynomial p(x)∈Q[x] of degree at most d. In particular, the above sequence is an arithmetic progression when d=1. In this paper, we show the asymptotic density of such numbers n as above. When d=1, the asymptotic density is equal to 1/(k−1). Although the common difference r is arbitrarily fixed in the above result, we also examine the case when r is not fixed. Most results in this paper are generalized by using functions belonging to Hardy fields." @default.
- W3086273891 created "2020-09-21" @default.
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- W3086273891 date "2021-05-01" @default.
- W3086273891 modified "2023-09-23" @default.
- W3086273891 title "Distributions of finite sequences represented by polynomials in Piatetski-Shapiro sequences" @default.
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- W3086273891 doi "https://doi.org/10.1016/j.jnt.2020.12.004" @default.
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