Abstract
The approximation theory of algebraic numbers by rationals or algebraic numbers occupies an important part in Diophantine approximation theory. After C.F. Osgood’s observation, P. Vojta formulated an analogue of Nevanlinna theory and Diophantine approximation theory and proposed the so-called Vojta conjecture in Diophantine approximation theory which corresponds to Nevanlinna’s Second Main Theorem. In this chapter, referring the proofs of results of the Diophantine approximation to other literature, we formulate them in view of Nevanlinna theory which has been discussed up to the present point. As an application we will prove some theorems on rational points which are analogous to those obtained in Chaps. 7 and 8; the analogy will be observed not only in the statements but also in their proofs.
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Notes
- 1.
Cf. the footnote to Theorem 4.9.7.
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Noguchi, J., Winkelmann, J. (2014). Diophantine Approximation. In: Nevanlinna Theory in Several Complex Variables and Diophantine Approximation. Grundlehren der mathematischen Wissenschaften, vol 350. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54571-2_9
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DOI: https://doi.org/10.1007/978-4-431-54571-2_9
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