Abstract
Motivated by [19] and [10], we define the modified proximity function \(\overline{m}_{q}(f,r)\) for entire curves in complex projective space \(\mathbf{P}^n\mathbf{C}\), and establish an asymptotic equality of Cartan's Second Main Theorem. This is a generalization of [19, Theorem 1.6] for transcendental meromorphic functions. Moreover, we strengthen the result to entire curves of finite order and holomorphic mappings over multiple variables.
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Acknowledgement
I would like to thank Professor Songyan Xie for recommanding me the article [19]. I also thank Dr. Zhangchi Chen, Bin Guo et al. for their interests in this work and some useful discussions. This paper was completed when I was attending the seminars in Academy of Mathematics and Systems Science (AMSS) in Beijing. So I would like to thank AMSS and its staff for their hospitality. I would like to thank Professor Min Ru and Professor Katsutoshi Yamanoi for their comments and some advice on the manuscript. I am also grateful to Professor Qiming Yan and Professor Guangyuan Zhang for their supports and encouragements.
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Chen, Y. An asymptotic equality of Cartan's Second Main Theorem and some generalizations. Anal Math (2024). https://doi.org/10.1007/s10476-024-00043-8
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DOI: https://doi.org/10.1007/s10476-024-00043-8