On r-free integers in Beatty sequences

Kim, Veasna; Srichan, Teerapat; Mavecha, Sukrawan

doi:10.1007/s40590-022-00422-x

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2022

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“…where A = max{τ (m), 1 ≤ m ≤ x 2 }, and α > 1 is fixed irrational algebraic number. More recently, Kim, Srichan and Mavecha [9] improved the above result by showing that…”

Section: Introductionmentioning

confidence: 80%

On $k$-free numbers over Beatty sequences

Zhang¹

2022

Preprint

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In this paper, we consider k-free numbers over Beatty sequences. New results are given. In particular, for a fixed irrational number α > 1 of finite type τ < ∞, any constant ε > 0, we can show thatwhere Q k is the set of positive k-free integers and the implied constant depends only on α, ε, k and β. This improves previous results. The main new ingredient of our idea is an employing of the double exponential sums of the type 1≤h≤H 1≤n≤x n∈Q k e(ϑhn).

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“…where A = max{τ (m), 1 ≤ m ≤ x 2 }, and α > 1 is fixed irrational algebraic number. More recently, Kim, Srichan and Mavecha [9] improved the above result by showing that…”

Section: Introductionmentioning

confidence: 80%

On $k$-free numbers over Beatty sequences

Zhang¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

On r-free integers in Beatty sequences

Cited by 1 publication

References 7 publications

On $k$-free numbers over Beatty sequences

On $k$-free numbers over Beatty sequences

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