2023
DOI: 10.1112/plms.12570
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Functions tiling simultaneously with two arithmetic progressions

Mark Mordechai Etkind,
Nir Lev

Abstract: We consider measurable functions on that tile simultaneously by two arithmetic progressions and at respective tiling levels and . We are interested in two main questions: what are the possible values of the tiling levels , and what is the least possible measure of the support of ? We obtain sharp results which show that the answers depend on arithmetic properties of and , and in particular, on whether the numbers are rationally independent or not.

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