|
Regularity of growth and the class 
Author(s):
D.
Drasin
Journal:
Conform. Geom. Dyn.
11
(2007),
90-100.
Posted:
June 11, 2007
Errata:
Conform. Geom. Dyn. 12 (2008), 187.
MathSciNet review:
2314244
Retrieve article in:
PDF
Abstract |
References |
Additional information
Abstract:
Given  , there is an entire function  in the Speiser class  of order  , lower order  .  may have as few as three singular values.
References:
-
- [1]
- I. N. BAKER, J. KOTUS, Y L¨U, Iterates of meromorphic functions. IV. Critically finite functions, Results Math 22 (1992), 651-656. MR 1189754 (94c:58166)
- [2]
- W. BERGWEILER, A. EREMENKO, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana 11 (1995), 355-373. MR 1344897 (96h:30055)
- [3]
- D. DRASIN, A. WEITSMAN, Meromorphic functions with large sums of deficiencies, Advances in Math 15 (1975), 93-126. MR 0355051 (50:7528)
- [4]
- A. EREMENKO, M. YU. LYUBICH, Dynamical properties of some classes of entire functions, Ann. Inst. Fourier (Grenoble) 42 (1992), 989-1020. MR 1196102 (93k:30034)
- [5]
- H. K¨UNZI, H. WITTICH, The distribution of
 -points of certain meromorphic functions, Mich. Math. J. 6 (1959), 105-121. MR 0104808 (21:3561) - [6]
- S. MERENKOV, Rapidly growing entire functions with three singular values, preprint.
- [7]
- O. TEICHMÜLLER, Eine Umkehrung des zweiten Hauptsatzes der Wertverteilungslehre, Deutsche Mathematik 2 (1937), 96-107.
- [8]
- H. WITTICH, Neuere Untersuchungen über eindeutige analytische Funktionen (German) (Ergebnisse der Mathematik und ihrer Grenzgebite (N. F.) Heft 8), Springer Verlag, 1955. MR 0077620 (17:1067a)
Additional Information:
D.
Drasin
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
Email:
drasin@math.purdue.edu
DOI:
10.1090/S1088-4173-07-00159-2
PII:
S 1088-4173(07)00159-2
Received by editor(s):
July 11, 2006
Posted:
June 11, 2007
Additional Notes:
This work was initiated in 2001 when at the University of Nottingham, under SRC support. Presented December 3, 2005 at the Quasifest (Helsinki) in honor of the anniversaries of Seppo Rickman and Jussi Väisälä. The author thanks both Mathematics Departments for their hospitality and atmosphere.
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
