© 2001

Nevanlinna’s Theory of Value Distribution

The Second Main Theorem and its Error Terms


Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. William Cherry, Zhuan Ye
    Pages 1-4
  3. William Cherry, Zhuan Ye
    Pages 5-48
  4. William Cherry, Zhuan Ye
    Pages 49-88
  5. William Cherry, Zhuan Ye
    Pages 89-106
  6. William Cherry, Zhuan Ye
    Pages 107-117
  7. William Cherry, Zhuan Ye
    Pages 119-150
  8. William Cherry, Zhuan Ye
    Pages 161-186
  9. Back Matter
    Pages 187-203

About this book


On the one hand, this monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution because the authors only assume the reader is familiar with the basics of complex analysis. On the other hand, the monograph also serves as a valuable reference for the research specialist because the authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its "number theoretic digressions." These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.


Complex analysis Nevanlinna Nevanlinna theory approximation diophantine diophantine approximation error terms number theory value distribution

Authors and affiliations

  1. 1.Department of MathematicsUniversity of North TexasDentonUSA
  2. 2.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA

Bibliographic information

  • Book Title Nevanlinna’s Theory of Value Distribution
  • Book Subtitle The Second Main Theorem and its Error Terms
  • Authors William Cherry
    Zhuan Ye
  • Series Title Springer Monographs in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-66416-1
  • Softcover ISBN 978-3-642-08568-0
  • eBook ISBN 978-3-662-12590-8
  • Series ISSN 1439-7382
  • Edition Number 1
  • Number of Pages XII, 203
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Functions of a Complex Variable
    Several Complex Variables and Analytic Spaces
    Number Theory
  • Buy this book on publisher's site


From the reviews of the first edition:

"It is a phenomenon that value distribution theory is still a lively area of research. … As there is still need for further investigation which seems to require fundamentally new ideas, the authors were motivated to write this book. … The present book is very well written and it is a pleasure to read, especially the detailed motivations and comparisons of the different methods introduced and used in Nevanlinna theory." (Heinrich Begehr, Mathematical Reviews, Issue 2002 h)

"This book collects together the existing work on error terms. It gives an introduction to Nevanlinna’s theory of meromorphic functions, with an emphasis on error terms. … The book is very well-written. The reviewer highly recommends this book. To close on a personal note, I learned a lot from reading this book." (Min Ru, Zentralblatt MATH, Vol. 981, 2002)

"The book is a very nice introduction to the theory of value distribution by covering all major aspects of the theory. … One does not need too much prerequisite in reading the material, for the tools and concepts are introduced and explained in detail … . This is a very valuable book that may be interesting both for researchers in function theory and number theory and for students." (Vilmos Totik, Acta Scientiarum Mathematicarum, Vol. 68, 2002)