Linear equations with two variables in Piatetski-Shapiro sequences

2020/11/10 by Kota Saito, Saito, Kota
Mathematics · #Analytic and geometric function theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Number Theory (math.NT) #Primary:11D04 #Secondary:11K55

paper · pdf · doi:10.48550/arxiv.2011.05069

openalex publication_date 2020/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every non-integral α>1, the sequence of the integer parts of n^α (n=1,2,…) is called the Piatetski-Shapiro sequence with exponent α, and let PS(α) denote the set of all those terms. For all X⊆ ℕ, we say that an equation y=ax+b is solvable in X if the equation has infinitely many solutions of distinct pairs (x,y)∈ X². Let a,b∈ ℝ with a≠ 1 and 0≤ b

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