Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the multiple points of certain meromorphic functions


Author: J. K. Langley
Journal: Proc. Amer. Math. Soc. 123 (1995), 1787-1795
MSC: Primary 30D35
MathSciNet review: 1242092
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that if f is transcendental and meromorphic in the plane and $ T(r,f) = o{(\log r)^2}$, then f has infinitely many critical values. This is sharp. Further, we apply a result of Eremenko to show that if f is meromorphic of finite lower order in the plane and $ N(r,1/ff'') = o(T(r,f' /f))$, then $ f(z) = \exp (az + b)$ or $ f(z) = {(az + b)^{ - n}}$ with a and b constants and n a positive integer.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30D35

Retrieve articles in all journals with MSC: 30D35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1242092-4
PII: S 0002-9939(1995)1242092-4
Article copyright: © Copyright 1995 American Mathematical Society