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arXiv · 2404.05455

Minimal gap for higher dimensional sequences

Tanmoy Bera
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Abstract

In this note, we extend the notion of minimal gaps to the higher dimensional sequences. We bound the minimal gap for $(\{\boldsymbol{a}_n\boldsymbol{\alpha}\}),$ $(\{a_n\boldsymbol{\alpha}\})$ and $(\{\boldsymbol{a}_n\cdot\boldsymbol{\alpha}\})$ in terms of cardinality of the difference set of $a_n$ and $\boldsymbol{a}_n,$ where $a_n$ and $a_n^{(1)},\dots,a_n^{(d)}$ are sequences of distinct integers.

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Tanmoy Bera. 2024-04-08. Minimal gap for higher dimensional sequences. https://doi.org/10.1007/s40993-026-00747-w

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