Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-12T10:07:17.431Z Has data issue: false hasContentIssue false
  • English
  • Français

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: pgjameson2@gmail.com

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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

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

Information

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

References

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