Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the area of the region where an entire function is greater than one


Author: Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 102 (1988), 68-70
MSC: Primary 30D15,; Secondary 30D20
MathSciNet review: 915718
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using Carleman's inequality, we prove that if $ f$ is entire and of finite order $ \rho \geq 1$, then

$\displaystyle \mathop {\lim \,sup}\limits_{r \to \infty } \frac{{A(r)}}{{{r^2}}} \geq \frac{\pi }{{2\rho }},$

where $ A(r)$ is the area of the region $ \{ z:\vert f(z)\vert \geq 1\;{\text{and}}\;\vert z\vert \leq r\} $.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D15,, 30D20

Retrieve articles in all journals with MSC: 30D15,, 30D20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0915718-6
Article copyright: © Copyright 1988 American Mathematical Society