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A generalization of a result on maximum modulus of polynomials

V. K. Jain


Puni tekst: engleski pdf 140 Kb

str. 269-272

preuzimanja: 89

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Sažetak

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).

Ključne riječi

Polynomials; zeros; geometric mean; maximum modulus

Hrčak ID:

1320

URI

https://hrcak.srce.hr/1320

Datum izdavanja:

1.12.2003.

Posjeta: 441 *