Abstract
In this survey paper, we discuss the recent development of Nevanlinna theory of meromorphic functions on annuli, which extends results in Nevanlinna theory in the complex plane or in a disk. In particular, we show that the approach taken on annuli is a unified treatment of functions meromorphic in the complex plane, a disk and an annulus. It allows one to obtain many results in the complex plane and in a disk as corollaries of our results in annuli.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bank S, Laine I, Representations of solutions of periodic second order linear differential equations. J Reine Angew Math, 1983, 344: 1–21
Bieberbach L. Theorie der gewöhnlichen Differentialgleichungen. Berlin: Springer-Verleg, 1965
Cherry W, Ye Z. Nevanlinna’s Theory of Value Distribution. New York: Springer, 2001
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, 2007, 27: 273–290
Gol’dberg A, Grinshtein A. The logarithmic derivative of a meromorphic function. Mat Zametki, 1976, 19: 525–530 (in Russian); English translation in: Math Notes, 1976, 19: 320–323
af Hällström G. Über meromorphe Funktionen mit mehrfach zusammenhängenden Existenzgebieten. Acta Acad Aboensis Math Phys, 1940, 12: 1–100
Hanyak M O, Kondratyuk A A. Meromorphic functions in m-punctured complex planes. Mat Stud, 2007, 27: 53–69
Hayman W. Meromorphic Functions. Oxford: Clarendon Press, 1964
Hayman W, Yang L. Growth and values of functions regular in an angle. Proc London Math Soc (3), 1982, 44: 193–214
Khrystiyanyn Ya A, Kondratyuk A A. On the Nevanlinna theory for meromorphic functions on annuli, I. Mat Stud, 2005, 23: 19–30
Khrystiyanyn Ya A, Kondratyuk A A. On the Nevanlinna theory for meromorphic functions on annuli, II. Mat Stud, 2005, 24: 57–68
Kondratyuk A A, Laine I. Meromorphic functions in multiply connected domains. Univ Joensuu Dept Math Rep Ser, 2006, 10: 9–111
Korhonen R. Nevanlinna theory in an annulus, value distribution theory and related topics. Adv Complex Anal Appl, 2004, 3: 167–179
Lund M, Ye Z. Logarithmic derivatives in annuli. J Math Anal Appl, 2009, 356: 441–452
Lund M. Nevanlinna theory in Annuli. PhD Thesis. Dekalb: Northern Illinois University, 2009
Nevanlinna R. Analytic Functions. New York: Springer-Verlag, 1970
Selberg H. Über die ebenen Punktmengen von der Kapazität Null. Avh Norske Vid Akad Oslo, 1937, 10: 1–10
Valiron G. Lectures on the General Theory of Integral Functions. New York: Chelsea Publishing Company, 1949
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor Yang Lo on the Occasion of his 70th Birthday
Rights and permissions
About this article
Cite this article
Lund, M., Ye, Z. Nevanlinna theory of meromorphic functions on annuli. Sci. China Math. 53, 547–554 (2010). https://doi.org/10.1007/s11425-010-0037-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-010-0037-3