No CrossRef data available.
Article contents
The zeros of linear combinations of translates of polynomials
Published online by Cambridge University Press: 09 April 2009
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We investigate the location and separation of zeros of certain three-term linear combination of translates of polynomials. In particular, we find an interval of the form I = [−1, 1 + h], h > 0 such that for a polynomial f, all of whose zeros are real, and λ ∈ I, all zeros of f (x + 2ic) + 2λf (x) + f (x – 2ic) are also real.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 109 - 118
- Copyright
- Copyright © Australian Mathematical Society 2002
References
[1]Pólya, G., ‘Algebraische Untersuchungen über ganze Funktionen vom Geschlechte Null und Eins’, J. Reine Angew. Math. 145 (1915), 224–249.CrossRefGoogle Scholar
[2]Pólya, G., ‘Bemerkung über die Integraldarstellung der Riemannsche 
-Function’, Acta Math. 48 (1926), 305–317.CrossRefGoogle Scholar
-Function’, Acta Math. 48 (1926), 305–317.CrossRefGoogle Scholar[3]Walker, P. L., ‘Separation of the zeros of polynomials’, Amer. Math. Monthly 100 (1993), 272–273.Google Scholar
[4]Walker, P. L., ‘Bounds for the separation of real zeros of polynomials’, J. Austral. Math. Soc. (Series A) 59 (1995), 330–342.CrossRefGoogle Scholar
[5]Walker, P. L., ‘Separation of zeros of translates of polynomials and entire functions’, J. Math. Anal. Appl. 206 (1997), 270–279.CrossRefGoogle Scholar
You have
Access