zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the Nevanlinna direction of an algebroid function dealing with multiple values. (English) Zbl 1142.30329
Summary: By using Ahlfors’ theory of covering surfaces, we prove that for an algebroid function $w(z)$ satisfying $\limsup_{r\to\infty}T(r,w)/\log^2r=+\infty$, there exists at least one Nevanlinna direction dealing with multiple values.

MSC:
30D35Distribution of values (one complex variable); Nevanlinna theory
WorldCat.org
Full Text: DOI
References:
[1] Hayman, W. K.: Meromorphic functions. (1964) · Zbl 0115.06203
[2] Tsuji, M.: Potential theory in modern function theory. (1959) · Zbl 0087.28401
[3] Selberg, H.: Über eine eigenschaft der logarithmischen ableitung einer meromorphen oder algebroide funktion endlicher ordnung. Avh. norske vid. Akad. Oslo I 14 (1929) · Zbl 55.0779.04
[4] Selberg, H.: Über die wertverteilung der algebroiden funktionen. Math. Z. 31, 709-728 (1930) · Zbl 56.0280.06
[5] Ullrich, E.: Über den einfluss der verzweigtheit einer algebroide auf ihre wertverteilung. J. reine angew. Math. 169, 198-220 (1931) · Zbl 0003.21202
[6] Valiron, G.: Sur quelques propriétés des fonctions algébroıdes. C. R. Acad. sci. Paris 189, 824-826 (1929) · Zbl 55.0200.01
[7] Valiron, G.: Sur LES directions de Borel des fonctions algébroıdes méromorphes d’ordre infini. C. R. Acad. sci. Paris 206, 735-737 (1938) · Zbl 64.0300.03
[8] Rauch, A.: Sur LES algébroıdes entières. C. R. Acad. sci. Paris 202, 2041-2043 (1936) · Zbl 62.0365.01
[9] Toda, N.: Sur LES directions de Julia et de Borel des fonctions algébroıdes. Nagoya math. J. 34, 1-23 (1969) · Zbl 0174.12002
[10] Lü, Y. N.; Gu, Y. X.: On the existence of Borel direction for algebroidal function. Sc. bull. 28, 264-266 (1983)
[11] Lü, Y. N.; Zhang, G. H.: On Nevanlinna direction of a meromorphic function. Sci. sinica ser. A 26, 607-617 (1983)
[12] Sun, D. C.: The existence theorem of the Nevanlinna direction. Chinese ann. Math. ser. A 7, No. 2, 212-221 (1986) · Zbl 0604.30036
[13] Lu, Q.; Gu, Y. X.: On Nevanlinna directions of algebroid functions. Acta math. Sinica B 25, No. 2, 367-375 (2005) · Zbl 1088.30020
[14] Gao, Z. S.; Wang, F. Z.: Theorems of the covering surfaces and multiple values of the algebroid functions. Acta math. Sinica 44, 805-814 (2001) · Zbl 1125.30309
[15] He, Y. Z.; Xiao, X. Z.: Algebroid functions and ordinary differential equations. (1988)