The Journal of the Indian Mathematical Society

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On Maximum Modulus of Polynomials With Zeros in the Closed Exterior of a Circle


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1 Mathematics Department, I.I.T., Kharagpur-721302, India
     

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Let f(z) be an arbitrary entire function and M(f,r)=max |f(z)|. If p(z) is a polynomial of degree n, having no zeros in |zl<k≤1, with M(p,1)=1, then for k=1, it is known that.
M(p,R)≤Rn+1/2, R>1.
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  • On Maximum Modulus of Polynomials With Zeros in the Closed Exterior of a Circle

Abstract Views: 213  |  PDF Views: 0

Authors

V. K. Jain
Mathematics Department, I.I.T., Kharagpur-721302, India

Abstract


Let f(z) be an arbitrary entire function and M(f,r)=max |f(z)|. If p(z) is a polynomial of degree n, having no zeros in |zl<k≤1, with M(p,1)=1, then for k=1, it is known that.
M(p,R)≤Rn+1/2, R>1.