Can you hear the shape of a Beatty sequence?

dc.creatorGraham, Ron
dc.creatorO'Bryant, Kevin
dc.date2008-08-31
dc.date.accessioned2026-07-07T09:59:36Z
dc.date.available2026-07-07T09:59:36Z
dc.descriptionLet K(x_1,...,x_d) be a polynomial. If you are not given the real numbers α_1, α_2, ...,α_d, but are given the polynomial K and the sequence a_n=K(\floor{nα_1},\floor{nα_2},...,\floor{nα_d}), can you deduce the values of α_i? Not, it turns out, in general. But with additional irrationality hypotheses and certain polynomials, it is possible. We also consider the problem of deducing α_i from the integer sequence with nested flooring (\floor{\floor{... \floor{\floor{nα_1}α_2}... α_{d-1}}α_d})_{n=1}^\infty.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/0809.0004
dc.identifierhttp://arxiv.org/abs/0809.0004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168081
dc.subjectNumber Theory
dc.subjectDynamical Systems
dc.titleCan you hear the shape of a Beatty sequence?
dc.typetext

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