Springer Monographs in Mathematics

Nevanlinna’s Theory of Value Distribution

The Second Main Theorem and its Error Terms

Authors: Cherry, William, Ye, Zhuan

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eBook 71,39 €
price for Spain (gross)
  • ISBN 978-3-662-12590-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 88,35 €
price for Spain (gross)
  • ISBN 978-3-540-66416-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,35 €
price for Spain (gross)
  • ISBN 978-3-642-08568-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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.

Reviews

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)


Table of contents (8 chapters)

  • Introduction

    Cherry, William (et al.)

    Pages 1-4

    Preview Buy Chapter 30,19 €
  • The First Main Theorem

    Cherry, William (et al.)

    Pages 5-48

    Preview Buy Chapter 30,19 €
  • The Second Main Theorem via Negative Curvature

    Cherry, William (et al.)

    Pages 49-88

    Preview Buy Chapter 30,19 €
  • Logarithmic Derivatives

    Cherry, William (et al.)

    Pages 89-106

    Preview Buy Chapter 30,19 €
  • The Second Main Theorem via Logarithmic Derivatives

    Cherry, William (et al.)

    Pages 107-117

    Preview Buy Chapter 30,19 €

Buy this book

eBook 71,39 €
price for Spain (gross)
  • ISBN 978-3-662-12590-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 88,35 €
price for Spain (gross)
  • ISBN 978-3-540-66416-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 88,35 €
price for Spain (gross)
  • ISBN 978-3-642-08568-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Nevanlinna’s Theory of Value Distribution
Book Subtitle
The Second Main Theorem and its Error Terms
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2001
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-12590-8
DOI
10.1007/978-3-662-12590-8
Hardcover ISBN
978-3-540-66416-1
Softcover ISBN
978-3-642-08568-0
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 203
Topics