The subject of the book is Diophantine approximation and
Nevanlinna theory. Not only does the text provide new results and
directions, it also challenges open problems and collects latest
research activities on these subjects made by the authors over the
past eight years. Some of the significant findings are the proof of
the Green-Griffiths conjecture by using meromorphic connections and
Jacobian sections, and a generalized abc-conjecture. The book also
presents the state of the art in the studies of the analogues
between Diophantine approximation (in number theory) and value
distribution theory (in complex analysis), with a method based on
Vojta's dictionary for the terms of these two fields. The
approaches are relatively natural and more effective than existing
methods.
The book is self-contained and appended with a comprehensive and
up-to-date list of references. It is of interest to a broad
audience of graduate students and researchers specialized in pure
mathematics.
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