Glasnik Matematicki, Vol. 33, No.1 (1998), 33-36.
CERTAIN INTERESTING IMPLICATIONS OF T. J.
RIVLIN'S RESULT ON MAXIMUM MODULUS OF A POLYNOMIAL
V. K. Jain
Mathematics Department, I.I.T., Kharagpur - 721302, India
Abstract. Let f(z) be an arbitrary
entire function and M(f,r) =
|f(z)|. For a polynomial p(z) of degree
n, having no zeros in |z| < 1, Rivlin had obtained
r ≤ 1.
Using this and various associated results, we have obtained precise
and M(p,1) for polynomials p(z) having
all its zeros on |z| = k, k > 0. Some sort of a
converse of Rivlin's result has also been obtained
1991 Mathematics Subject Classification.
Key words and phrases. Maximum modulus, zeros.
Full text (PDF) (free access)
Glasnik Matematicki Home Page