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)
Properties of differences of meromorphic functions. (English) Zbl 1224.30156
Summary: Let f be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference g(z)=f(z+c)-f(z) and the divided difference g(z)/f(z).
30D35Distribution of values (one complex variable); Nevanlinna theory
39A10Additive difference equations
30C15Zeros of polynomials, etc. (one complex variable)
[1]M. Ablowitz, R. G. Halburd and B. Herbst: On the extension of Painlevé property to difference equations. Nonlinearity 13 (2000), 889–905. · Zbl 0956.39003 · doi:10.1088/0951-7715/13/3/321
[2]W. Bergweiler and J. K. Langley: Zeros of differences of meromorphic functions. Math. Proc. Camb. Phil. Soc. 142 (2007), 133–147. · Zbl 1114.30028 · doi:10.1017/S0305004106009777
[3]W. Bergweiler and A. Eremenko: On the singularities of the inverse to a meromorphic function of finite order. Rev. Mat. Iberoamericana 11 (1995), 355–373. · Zbl 0830.30016 · doi:10.4171/RMI/176
[4]Z. X. Chen and K. H. Shon: On zeros and fixed points of differences of meromorphic functions. J. Math. Anal. Appl. 344-1 (2008), 373–383. · Zbl 1144.30012 · doi:10.1016/j.jmaa.2008.02.048
[5]Y. M. Chiang and S. J. Feng: On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane. Ramanujan J. 16 (2008), 105–129. · Zbl 1152.30024 · doi:10.1007/s11139-007-9101-1
[6]J. Clunie, A. Eremenko and J. Rossi: On equilibrium points of logarithmic and Newtonian potentials. J. London Math. Soc. 47-2 (1993), 309–320. · Zbl 0797.31002 · doi:10.1112/jlms/s2-47.2.309
[7]J. B. Conway: Functions of One Complex Variable. New York, Spring-Verlag.
[8]A. Eremenko, J. K. Langley and J. Rossi: On the zeros of meromorphic functions of the form Σ k=1 a k/(z z k). J. Anal. Math. 62 (1994), 271–286. · Zbl 0818.30020 · doi:10.1007/BF02835958
[9]G. Gundersen: Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. J. London Math. Soc. 37-2 (1988), 88–104.
[10]R. G. Halburd and R. Korhonen: Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J. Math. Anal. Appl. 314 (2006), 477–487. · Zbl 1085.30026 · doi:10.1016/j.jmaa.2005.04.010
[11]R. G. Halburd and R. Korhonen: Nevanlinna theory for the difference operator. Ann. Acad. Sci. Fenn. Math. 31 (2006), 463–478.
[12]W. K. Hayman: Meromorphic Functions. Oxford, Clarendon Press, 1964.
[13]W. K. Hayman: Slowly growing integral and subharmonic functions. Comment. Math. Helv. 34 (1960), 75–84. · Zbl 0123.26702 · doi:10.1007/BF02565929
[14]J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo and K. Tohge: Complex difference equations of Malmquist type. Comput. Methods Funct. Theory 1 (2001), 27–39. · doi:10.1007/BF03320974
[15]J. D. Hinchliffe: The Bergweiler-Eremenko theorem for finite lower order. Results Math. 43 (2003), 121–128. · doi:10.1007/BF03322728
[16]K. Ishizaki and N. Yanagihara: Wiman-Valiron method for difference equations. Nagoya Math. J. 175 (2004), 75–102.
[17]I. Laine: Nevanlinna Theory and Complex Differential Equations. Berlin, W. de Gruyter, 1993.
[18]L. Yang: Value Distribution Theory. Beijing, Science Press, 1993.
[19]C. C. Yang and H. X. Yi: Uniqueness Theory of Meromorphic Functions. Dordrecht, Kluwer Academic Publishers Group, 2003.