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

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

2002-09-16

arxiv.org/abs/math/0209204v1

Mathematics

Number Theory

14 pages

Scientific paper

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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