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Article
A Malmquist Type Theorem for a Class of Delay Differential Equations
We show that if the following delay differential equation of rational coefficients $$\begin{aligned} w^k(z)\sum _{\mu =1}^se_\mu (z)w(z+c_\mu ...
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Article
On Meromorphic Solutions of Functional Equations of Fermat Type
Take complex numbers \(\alpha ,\beta ,c,a_j,b_j\) ...
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Article
Normality Criteria of Meromorphic Functions Sharing a Holomorphic Function
Take three integers \(m\ge 0,\,k\ge 1\) m ...
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Article
A Note on Meromorphic Solutions of Linear Partial Differential Equations of Second Order
We will prove a uniqueness theorem for meromorphic solutions of linear partial differential equations of second order with polynomial coefficients associated with the Jacobi differential equations and their ge...
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Article
Bounds of discriminants of number fields
In this survey, we introduce some progress on bounds of discriminants of number fields which contains the Rogers-Mulholland’s improvement of Minkowski’s classic inequality obtained by using geometry of numbers...
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Article
Unicity of meromorphic solutions of partial differential equations
In this survey, results on the existence, growth, uniqueness, and value distribution of meromorphic (or entire) solutions of linear partial differential equations of the second order with polynomial coefficien...
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Article
Subspace theorems for homogeneous polynomial forms
We prove a subspace theorem for homogeneous polynomial forms which generalizes Schmidt’s subspace theorem for linear forms. Further, we formalize the subspace theorem into a form which is just the counterpart ...
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Book
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Chapter
Jet Bundles and its Applications in Value Distribution of Holomorphic Map**s
In this paper, we have established the technique of the higher dimensional jets and applied the results to study value distribution of holomorphic map**s. As applications, we have also generalized the result...
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Chapter and Conference Paper
Nevanlinna Theory and Diophantine Approximations
In this note, we will introduce some basic problems and progresses in Nevanlinna theory and Diophantine approximations, say, discuss the abc-conjecture and Hall’s conjecture for integers, and prove their analogue...
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Book
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Chapter
Nevanlinna theory
In this chapter, we will introduce notations, terminologies and basic tools used in this book. In particular, we mainly introduce the Nevanlinna theory, that is, value distribution theory, which plays key rule...
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Chapter
Uniqueness of meromorphic functions on ℂ m
In this chapter we shall concentrate on the uniqueness questions of meromorphic functions on ℂ m . Mainly, we will extend some well-known uniqueness theorems on one complex variable ...
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Chapter
Algebroid functions of several variables
Beginning with Valiron [262], the value distribution theory of algebroid functions of one complex variable has been studied extensively. A few contributions are listed under references. The Nevalinna theory of...
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Chapter
Uniqueness of meromorphic functions on ℂ
Combining value distribution theory and the classical function theory to study uniqueness theorems of meromorphic functions has become an interesting and active field in recent years. Nevanlinna himself proved...
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Chapter
Uniqueness of meromorphic map**s
In this chapter, we will introduce some well-known uniqueness theorems of meromorphic map**s between complex manifolds. Basic methods are more general value distribution theory, which will be introduced in S...
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Book
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Chapter
Differential equations
In this chapter, we will give a survey of the non-Archimedean analogue of Malmquist-type theorems in ordinary differential equations based on the results of Yang-Hu [138].
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Chapter
Defect Relations for Moving Targets
In this paper, we extend the general defect relation of the associated curves of a non-degenerate holomorphic curve to moving targets. Our results also improve the corresponded defect relations of Stoll for th...
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Chapter
Elimination of Defects of Non-Archchimedean Holomorphic Curves
In this paper, we will prove that for any transcendental holomorphic curve f :k → ℙ n (k) where k is an algebraically closed field of characteristic zero, complete for a non-trivial...
