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Diophantine properties of the zeros of certain Laguerre and para-Jacobi polynomials

Journal of Physics A: Mathematical and Theoretical, ISSN: 1751-8113, Vol: 45, Issue: 9
2012
  • 11
    Citations
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  • 6
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Metrics Details

  • Citations
    11
    • Citation Indexes
      11
  • Captures
    6

Article Description

Matrices A and B of arbitrary rank N, given by simple expressions in terms of the N zeros of certain Laguerre or para-Jacobi polynomials of degree N, feature a Diophantine property. In the Laguerre case, this property states that the 2N zeros of the polynomial p (Λ) = det[Λ + ΛA + B]are all integers; indeed we conjecture that det[Λ + ΛA + B]= Π [Λ ? k ]. The results in the para-Jacobi case are somewhat analogous; they refer to the zeros of the general solution of the ODE generally characterizing Jacobi polynomials, in the special case in which this solution is a para-Jacobi polynomial featuring an additional, arbitrary parameter. © 2012 IOP Publishing Ltd.

Bibliographic Details

Francesco Calogero; Ge Yi

IOP Publishing

Physics and Astronomy; Mathematics

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