Abstract
In this article several theorems of the theory of Γ-lines for meromorphic functions are extended to the more general setting of algebroid functions. We recall the definition of algebroid function of order k and how it can be considered as a function defined on a Riemann surface of k sheets. In this way, we prove the so called tangent variation principle for algebroid functions, previously proved for meromorphic functions by Barsegian, and we get several consequences of this result. We also extend a proposition on proximity properties of meromorphic functions.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Barsegian G.: A proximity property of the a-points of meromorphic functions. Math. URSS Sbornik 48(1), 41–63 (1984)
Barsegian G.: Γ-lines. On the Geometry of Real and Complex Functions. Taylor & Francis, London (2002)
Fernández Arias A.: The error term in Nevanlinna’s second fundamental theorem for holomorphic mappings on coverings. Rev. R. Acad. Cien. Serie A. Mat. 96(1), 7–21 (2002)
Lang, S., Cherry, W.: Topics in Nevanlinna theory. In: Lecture Notes in Mathematics, vol. 1433. Springer, New York (1990)
Miles J.: Bounds on the ratio n(r, a)/S(r) for meromorphic functions. Trans. Am. Math. Soc. 162, 383–393 (1971)
Selberg H.L.: Algebroide Funktionen und Umkehrfunktionen Abelscher Integrale. Avh. Norske. Vid. Akad. Oslo 8, 1–72 (1934)
Ullrich E.: Über den Einfluss der Verzweigtheit einer Algebroide auf ihre Wertverteilung. Journal für die reine und angewandte Mathematik 169, 198–220 (1931)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Lucian Beznea.
A. Fernández Arias was partially supported by the project MTM2009-09501 of the Spanish Ministry of Education.
Rights and permissions
About this article
Cite this article
Alonso Gómez, A., Fernández Arias, A. Γ-Lines of Algebroid Functions. Complex Anal. Oper. Theory 5, 847–861 (2011). https://doi.org/10.1007/s11785-010-0105-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11785-010-0105-2