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Diophantine Approximations and Value Distribution Theory

Paul Vojta
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TLDR
In this article, the main conjecture and the ramification term of the conjecture are discussed. But they do not consider the relation between Nevanlinna theory and hyperplanes, unlike the main conjectures of this paper.
Abstract
Heights and integral points.- Diophantine approximations.- A correspondence with Nevanlinna theory.- Consequences of the main conjecture.- The ramification term.- Approximation to hyperplanes.

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Value Distribution of Meromorphic Functions

TL;DR: A survey of results after 1970 can be found in this paper, where the authors present a survey of meromorphic functions of finite-order functions with respect to Riemann surfaces.
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On the extension of the Painlevé property to difference equations

TL;DR: In this paper, it is argued that the integrability of many difference equations is related to the structure of their solutions at infinity in the complex plane and that Nevanlinna theory provides many of the concepts necessary to detect integranability in a large class of equations.

Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials

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Uniformity of rational points

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