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The maximum modulus of a complex polynomial on the unit circle

Published online by Cambridge University Press:  17 February 2025

G.J.O. Jameson
G.J.O. Jameson*
Affiliation:
13 Sandown Road, Lancaster LA1 4LN e-mail: [email protected]
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Extract

Consider a complex polynomial $$f(z) = \sum\nolimits_{r = 0}^n {{a_r}{z^r}} $$. Define

$$M(f) = {\rm sup}\left\{ {\left| {f(z)} \right|:\left| z \right| \le 1} \right\}.$$

Type
Articles
Information
The Mathematical Gazette , Volume 109 , Issue 574 , March 2025 , pp. 119 - 123
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Copyright
© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Shapiro, H. S., Extremal problems for polynomials and power series, Thesis for master's degree, Massachusetts Institute of Technology (1951).Google Scholar