99 research outputs found
Spectral Factorization of Trigonometric Polynomials and Lattice Geometry
We formulate a conjecture concerning spectral factorization of a class of
trigonometric polynomials of two variables and prove it for special cases. Our
method uses relations between the distribution of values of a polynomial of two
variables and the distributions of values of an associated family of
polynomials of one variable. We suggest an approach to prove the full
conjecture using relations between the distribution of values and the
distribution of roots of polynomials.Comment: This paper has been accepted for publication in Acta Arithmetica, it
is a thoroughly revised and retitled version of the arXiv:1110.5277 paper
submitted on 24 Oct 2011 that was titled "Spectral Factorization and Lattice
Geometry
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