## Certain applications of the theory of polar-composite polynomials

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- by Neyamat Zaheer and Mahfooz Alam PDF
- Proc. Amer. Math. Soc.
**85**(1982), 383-388 Request permission

## Abstract:

In a recent paper [**5**] the authors have, for the first time, given a detailed account of the theory of polar-composite polynomials in algebraically closed fields of characteristic zero. In another paper [

**6**], we have given some applications of this theory and have obtained a few results for a new variety of composite polynomials which have been derived from certain polar-composite polynomials through iteration. In the present paper also we consider the same variety of composite polynomials, but our present study deals with a different aspect of application of the said theory. Besides other things, our main theorem here offers a generalization of a result due to Marden [

**2**] (see also [

**1**, Theorem (16,3)]).

## References

- Morris Marden,
*Geometry of polynomials*, 2nd ed., Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR**0225972** - Morris Marden,
*The zeros of certain composite polynomials*, Bull. Amer. Math. Soc.**49**(1943), 93–100. MR**7809**, DOI 10.1090/S0002-9904-1943-07856-1
N. Zaheer, - Neyamat Zaheer,
*On polar relations of abstract homogeneous polynomials*, Trans. Amer. Math. Soc.**218**(1976), 115–131. MR**401719**, DOI 10.1090/S0002-9947-1976-0401719-X - Neyamat Zaheer and Mahfooz Alam,
*Zeros of polar-composite polynomials in algebraically closed fields*, Proc. London Math. Soc. (3)**40**(1980), no. 3, 527–552. MR**572018**, DOI 10.1112/plms/s3-40.3.527 - Neyamat Zaheer and Mahfooz Alam,
*Some applications of the theory of polar-composite polynomials*, J. London Math. Soc. (2)**22**(1980), no. 3, 403–410. MR**596319**, DOI 10.1112/jlms/s2-22.3.403 - Spiros P. Zervos,
*Aspects modernes de la localisation des zéros des polynomes d’une variable*, Ann. Sci. École Norm. Sup. (3)**77**(1960), 303–410 (French). MR**0125944**

*Null-sets of abstract homogeneous polynomials in vector spaces*, Doctoral thesis, Univ. of Wisconsin, Milwaukee, 1971.

## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**85**(1982), 383-388 - MSC: Primary 30C15
- DOI: https://doi.org/10.1090/S0002-9939-1982-0656108-8
- MathSciNet review: 656108