Functions tiling simultaneously with two arithmetic progressions

Mark Mordechai Etkind, Nir Lev

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Pages (from-to)1775-1815
Number of pages41
JournalProceedings of the London Mathematical Society
Issue number6
StatePublished - Dec 2023

Bibliographical note

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© 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.


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