Abstract
In this paper we study the irregularities of distribution of subsets of integer vectors relative to higher dimensional arithmetic progressions. In particular we give one-sided estimate of the discrepancies of subsets of d-dimensional cubes, i.e. we show that these discrepancies have both large positive and small negative values.
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Acknowledgments
Research partially supported by Hungarian National Foundation for Scientific research, Grant No. K100291 and by the Momentum (Lendület) Fund of the Hungarian Academy of Science.
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Mérai, L. The higher dimensional analogue of certain estimates of Roth and Sárközy. Period Math Hung 68, 77–91 (2014). https://doi.org/10.1007/s10998-014-0016-5
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DOI: https://doi.org/10.1007/s10998-014-0016-5