Matrices (A) under bar and (B) under bar 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(2N) (lambda) = det[lambda(2) + lambda(A) under bar + (B) under bar] are all integers; indeed we conjecture that det [lambda(2) + lambda(A) under bar + (B) under bar] = Pi(N)(k=1) (lambda(2) - k(2)). 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.

Diophantine properties of the zeros of certain Laguerre and para-Jacobi polynomials / Calogero, Francesco; Yi, Ge. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 45:9(2012), p. 095207. [10.1088/1751-8113/45/9/095207]

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

CALOGERO, Francesco;
2012

Abstract

Matrices (A) under bar and (B) under bar 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(2N) (lambda) = det[lambda(2) + lambda(A) under bar + (B) under bar] are all integers; indeed we conjecture that det [lambda(2) + lambda(A) under bar + (B) under bar] = Pi(N)(k=1) (lambda(2) - k(2)). 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
01 Pubblicazione su rivista::01a Articolo in rivista
Diophantine properties of the zeros of certain Laguerre and para-Jacobi polynomials / Calogero, Francesco; Yi, Ge. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 45:9(2012), p. 095207. [10.1088/1751-8113/45/9/095207]
File allegati a questo prodotto
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/435085
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 9
social impact