zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Logarithmic derivatives in annuli. (English) Zbl 1176.30080
The authors define Nevanlinna functions in annuli with two independent variables. They prove a version for annuli of Valiron’s decomposition theorem. Using this result and others proved in the paper a generalized logarithmic derivative lemma for annuli is established. This lemma includes the same for a disk and the complex plane.

30D35Distribution of values (one complex variable); Nevanlinna theory
Full Text: DOI
[1] Bank, S. B.; Laine, I.: Representations of solutions of periodic second order linear differential equations, J. reine angew. Math. 344, 1-21 (1983) · Zbl 0524.34007 · crelle:GDZPPN002200724
[2] Bieberbach, L.: Theorie der gewöhnlichen differentialgleichungen, (1965) · Zbl 0124.04603
[3] Cherry, W.; Ye, Z.: Nevanlinna’s theory of value distribution, (2001) · Zbl 0981.30001
[4] Chiang, Y. M.; Gao, S. A.: On a problem in complex oscillation theory of periodic second order linear differential equations and some related perturbation results, Ann. acad. Sci. fenn. Math. 27, No. 1, 273-290 (2002) · Zbl 1045.34057 · emis:journals/AASF/Vol27/chiang.html
[5] Gol’dberg, A. A.; Grinshtein, A.: The logarithmic derivative of a meromorphic function, Mat. zametki 19, 525-530 (1976)
[6] Hanyak, M. O.; Kondratyuk, A. A.: Meromorphic functions in m-punctured complex planes, Mat. stud. 27, No. 1, 53-69 (2007) · Zbl 1152.30027
[7] Khrystiyanyn, A. Ya.; Kondratyuk, A. A.: On the Nevanlinna theory for meromorphic functions on annuli, I, Mat. stud. 23, No. 1, 19-30 (2005) · Zbl 1066.30036
[8] Khrystiyanyn, A. Ya.; Kondratyuk, A. A.: On the Nevanlinna theory for meromorphic functions on annuli, II, Mat. stud. 24, No. 2, 57-68 (2005) · Zbl 1092.30048
[9] Kondratyuk, A. A.; Laine, I.: Meromorphic functions in multiply connected domains, Univ. Joensuu dept. Math. rep. Ser. 10, 9-111 (2006) · Zbl 1144.30013
[10] Korhonen, R.: Nevanlinna theory in an annulus, Adv. complex anal. Appl. 3, 167-179 (2004) · Zbl 1102.30025
[11] Korhonen, R.; Heittokangas, J.; Rättyä, J.: Generalized logarithmic derivative estimates of gol’dberg -- grinshtein type, Bull. London math. Soc. 36, 105-114 (2004) · Zbl 1067.30060 · doi:10.1112/S0024609303002649
[12] M. Lund, Nevanlinna theory for annuli, PhD thesis, Northern Illinois University, DeKalb, IL, 2009
[13] Valiron, G.: Lectures on the general theory of integral functions, (1949)
[14] Ye, Z.: On Nevanlinna’s second Main theorem in projective space, Invent. math. 122, No. 3, 475-507 (1995) · Zbl 0855.32002 · doi:10.1007/BF01231453