Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-16T01:29:08.660Z Has data issue: false hasContentIssue false
  • English
  • Français

The Second Mean Values of Entire Functions

Published online by Cambridge University Press:  20 November 2018

Q. I. Rahman
Q. I. Rahman*
Affiliation:
Université de Montréal
Rights & Permissions [Opens in a new window]

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.

Let f(z) be an entire function of the complex variable z = x + iy defined by the everywhere absolutely convergent Dirichlet series

1.1

If

then log m(x,f) is an increasing convex function of x (2), and

is called the Ritt order of f(z).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1113 - 1120
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Azpeitia, A. G., A remark on the Ritt order of entire functions defined by Dirichlet series, Proc. Amer. Math. Soc., 12 (1961), 722–723.Google Scholar
2. Doetsch, G., Über die obere Grenze des absoluten Betrages einer analytischen Funktion auf Geraden, Math. Zeitsch., 8 (1920), 237–240.Google Scholar
3. Gupta, J. S., On the mean values of integral functions and their derivatives defined by Dirichlet series, Amer. Math. Monthly, 71 (1964), 520–523.Google Scholar
4. Lakshminarasimhan, T. V., On a theorem concerning the means of an entire function and its derivative, J. London Math. Soc, 40 (1965), 305–308.Google Scholar
5. Rahman, Q. I., The Ritt order of the derivative of an entire function, Ann. Pol. Math., 17 (1965), 137–140.Google Scholar
6. Vijayaraghavan, T., On derivatives of integral functions, J. London Math. Soc, 10 (1935), 116–117.Google Scholar