© 2006

Value Distribution Theory Related to Number Theory


Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 1-87
  3. Pages 89-211
  4. Pages 213-285
  5. Pages 461-506
  6. Back Matter
    Pages 507-543

About this book


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.


Complex analysis Diophantine approximation Distribution Meromorphic function Nevanlinna theory diophantine equations number theory value distribution zeta function

Authors and affiliations

  1. 1.Department of MathematicsShandong UniversityJinan ShandongP.R. China
  2. 2.Department of MathematicsThe Hong Kong University of Science and TechnologyKowloon, Hong KongP.R. China

Bibliographic information

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From the reviews:

“In this monograph the authors survey both basics and well-known results of both value distribution theory in higher dimensions and Diophantine geometry. … This book is devoted to a subject the reviewer considers intriguing and it may be a valuable work of reference.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 154 (4), August, 2008)