Minimal gap for higher dimensional sequences

2024/04/08 by Bera, Tanmoy
#11J13 #11J71 #11J83 #11K31 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2404.05455

Abstract

In this note, we extend the notion of minimal gaps to the higher dimensional sequences. We bound the minimal gap for (\\boldsymbola_n\boldsymbolα\), (\a_n\boldsymbolα\) and (\\boldsymbola_n⋅\boldsymbolα\) in terms of cardinality of the difference set of a_n and \boldsymbola_n, where a_n and a_n⁽¹⁾,…,a_n^(d) are sequences of distinct integers.

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