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The number of unimodular roots of some reciprocal polynomials

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  • معلومة اضافية
    • بيانات النشر:
      Cellule MathDoc/CEDRAM, 2020.
    • الموضوع:
      2020
    • نبذة مختصرة :
      We introduce a sequence $P_{2n}$ of monic reciprocal polynomials with integer coefficients having the central coefficients fixed. We prove that the ratio between number of nonunimodular roots of $P_{2n}$ and its degree $d$ has a limit when $d$ tends to infinity. We present an algorithm for calculation the limit and a numerical method for its approximation. If $P_{2n}$ is the sum of a fixed number of monomials we determine the central coefficients such that the ratio has the minimal limit. We generalise the limit of the ratio for multivariate polynomials. Some examples suggest a theorem for polynomials in two variables which is analogous to Boyd's limit formula for Mahler measure.
      10 pages, 3 figures
    • File Description:
      .pdf
    • ISSN:
      1778-3569
    • الرقم المعرف:
      10.5802/crmath.28
    • Rights:
      OPEN
    • الرقم المعرف:
      edsair.doi.dedup.....d90da1d38130cbcd3fb7f362f398ac05