Unimodular roots of special littlewood polynomials Article

Mercer, ID. (2006). Unimodular roots of special littlewood polynomials . CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 49(3), 438-447. 10.4153/CMB-2006-043-x

cited authors

  • Mercer, ID



  • We call α(z) = a0 + a1z + ⋯ + a n-1zn-1 a Littlewood polynomial if aj = ±1 for all j. We call α(z) self-reciprocal if α(z) = z n-1α(1/z), and call α(z) skewsymmetric if n = 2m + 1 and am+j = (-1)jam-j for all j. It has been observed that Littlewood polynomials with particularly high minimum modulus on the unit circle in ℂ tend to be skewsymmetric. In this paper, we prove that a skewsymmetric Littlewood polynomial cannot have any zeros on the unit circle, as well as providing a new proof of the known result that a self-reciprocal Littlewood polynomial must have a zero on the unit circle. © Canadian Mathematical Society 2006.

publication date

  • January 1, 2006

Digital Object Identifier (DOI)

start page

  • 438

end page

  • 447


  • 49


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