Glasnik matematički, Vol. 38 No. 2, 2003.
Original scientific paper
A generalization of a result on maximum modulus of polynomials
V. K. Jain
Abstract
For an arbitrary entire function f(z)$, let M(f,d) = max|z|=d |f(z)|. It is known that if the geometric mean of the moduli of the zeros of a polynomial p(z) of degree n is at least 1, and M(p,1) = 1, then for R > 1, M(p,R) R/2 + 1/2 if n = 1,
M(p,R) Rn/2 + (3+22)Rn-2/2 if n 2.
We have obtained a generalization of this result, by assuming the geometric mean of the moduli of the zeros of the polynomial to be at least k, (k > 0).
Keywords
Polynomials; zeros; geometric mean; maximum modulus
Hrčak ID:
1320
URI
Publication date:
1.12.2003.
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