Polynomial root separation examples

• Autores: Arnold Schönhage
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 10, 2006, págs. 1080-1090
• Idioma: inglés
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• Resumen

  • In vol. 32 of this Journal, G.E. Collins reported on extensive calculations supporting his conjecture that the exponent in the well-known Mahler¿Mignotte bound for the root separation of squarefree integral polynomials of degree n might be replaceable with -n/2. This paper exhibits infinite sequences of cubic polynomials with ¿true¿ exponent -2, thus disproving that conjecture for degree n=3, and extends this to analogous bounds for close root triplets of quartic polynomials.