Linear Diophantine equations in Piatetski-Shapiro sequences

Volume: 200, Issue: 1, Pages: 91 - 110
Published: Jan 1, 2021
Abstract
A Piatetski-Shapiro sequence with exponent \alphais a sequence of integer parts of n^\alpha(n = 1,2,\ldots)with a non-integral \alpha > 0 We let \mathrm{PS}(\alpha)denote the set of those terms. In this article, we study the set of \alphaso that the equation ax + by = czhas infinitely many pairwise distinct solutions (x,y,z) \in \mathrm{PS}(\alpha)^3 and give a lower bound for its Hausdorff dimension. As a corollary, we...
Paper Details
Title
Linear Diophantine equations in Piatetski-Shapiro sequences
Published Date
Jan 1, 2021
Volume
200
Issue
1
Pages
91 - 110
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