ON A SUM INVOLVING CERTAIN ARITHMETIC FUNCTIONS ON PIATETSKI–SHAPIRO AND BEATTY SEQUENCES
Let 𝑐, 𝛼, 𝛽 ∈ R be such that 1<𝑐<2, 𝛼 > 1 is irrational and with bounded partial quotients, 𝛽 ∈ [0, 𝛼). In this paper, we study asymptotic behaviour of the summations of the form Σ_(n≤N) (f([n^c]))/([n^c]) and Σ_(n≤N) (f([𝛼n+𝛽]))/([𝛼n+𝛽]) , where f is the Euler totient function 𝜑, Dede...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2022-12-01
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| Series: | Проблемы анализа |
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| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=12210&lang=ru |