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- W3157879069 abstract "We extend to Segal–Piatetski-Shapiro sequences previous results on the Luca–Schinzel question. Namely, we prove that for any real c larger than 1, the sequence $$(sum _{mle n} varphi (lfloor m^c rfloor ) /lfloor m^c rfloor )_{nge 1}$$ is dense modulo 1, where $$varphi $$ denotes Euler’s totient function. The main part of the proof consists in showing that when R is a large integer, the sequence of the residues of $$lfloor m^c rfloor $$ modulo R contains any block of consecutive residues of a given length." @default.
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- W3157879069 date "2022-12-29" @default.
- W3157879069 modified "2023-10-02" @default.
- W3157879069 title "On a question of Luca and Schinzel over Segal–Piatetski-Shapiro sequences" @default.
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- W3157879069 doi "https://doi.org/10.1007/s11139-022-00684-z" @default.
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