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Spectra of certain types of polynomials and tiling of integers with translates of finite sets

Sergei Konyagin·Izabella Laba
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Abstract

We consider two number-theoretic problems arising from Fuglede's spectral set conjecture: characterizing finite sets that tile integers, and finding polynomials with (0,1) coefficients whose roots have a certain multiplicative structure. We verify several special cases of the relevant conjectures; in particular, we find necessary and sufficient conditions for a set A to tile the integers if A is a direct sum of cyclic subsets.

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Sergei Konyagin, Izabella Laba. 2002-09-16. Spectra of certain types of polynomials and tiling of integers with translates of finite sets. https://arxiv.org/abs/math/0209204

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