Difference Analogues of Second Main Theorem and Picard Type Theorem for Slowly Moving Periodic Targets
Download PDF
Authors: D. T. PHAM, D. T. NGUYEN AND T. T. LUONG
DOI: 10.46793/KgJMat2305.755P
Abstract:
In this paper, we show some Second main theorems for linearly nondegenerate meromorphic mappings over the field ????c1 of c-periodic meromorphic functions having their hyper-orders strictly less than one in ℂm intersecting slowly moving targets in ℙn(ℂ). As an application, we give some Picard type theorems for meromorphic mappings of ℂm into ℙn(ℂ) under the growth condition hyper-order less than one.
Keywords:
Second main theorem, meromorphic mappings, Nevanlinna theory, Casorati determinant, moving targets.
References:
[1] H. Cartan, Sur lés zeros des combinaisons linéaires de pfonctions holomorphes données, Mathematica Cluj 7 (1933), 5–31.
[2] T. B. Cao, Difference analogues of the second main theorem for meromorphic functions in several complex variables, Math. Nachr. 287(5-6) (2014), 530–545. https://doi.org/10.1002/mana.201200234
[3] T. B. Cao and R. Korhonen, A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables, J. Math. Anal. Appl. 444(2) (2016), 1114–1132. https://doi.org/10.1016/j.jmaa.2016.06.050
[4] H. Fujimoto, The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J. 58 (1975) 1–23.
[5] R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31(2) (2006), 463–478.
[6] P. M. Wong, H. F. Law and P. P. W. Wong, A second main theorem on ℙn for difference operator, Sci. China Ser. A-Math. 52(12) (2009), 2751–2758. https://doi.org/10.1007/s11425-009-0213-5
[7] R. Halburd, R. Korhonen and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Trans. Amer. Math. Soc. 366(8) (2014), 4267–4298. https://doi.org/10.1090/S0002-9947-2014-05949-7
[8] R. Korhonen, A difference Picard theorem for meromorphic functions of several variables, Comput. Methods Funct. Theory 12(1) (2012), 343–361. https://doi.org/10.1007/BF03321831
[9] R. Korhonen, N. Li and K. Tohge, Difference an anlogue of Cartan’s second main theorem for slowly moving periodic target, Ann. Acad. Sci. Fenn. Math. 41 (2016), 523–549. https://doi.org/10.5186/aasfm.2016.4131
[10] E. I. Nochka, On the theory of meromorphic functions, Sov. Math. Dokl. 27 (1983), 377–381.
[11] D. D. Thai and S. D.Quang, Second main theorem with truncated counting function in several complex variables for moving targets, Forum Math. 20 (2008), 163–179. https://doi.org/10.1515/FORUM.2008.007
Login:
