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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64967We 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.14 pagesNumber Theory11A99Spectra of certain types of polynomials and tiling of integers with translates of finite setstext