Skip to main content
SpringerLink
Log in
Book cover

Nevanlinna’s Theory of Value Distribution

The Second Main Theorem and its Error Terms

  • Book
  • © 2001

Overview

Authors:
  1. William Cherry

    1. Department of Mathematics, University of North Texas, Denton, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Zhuan Ye

    1. Department of Mathematical Sciences, Northern Illinois University, DeKalb, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction

    • William Cherry, Zhuan Ye
    Pages 1-4

  3. The First Main Theorem

    • William Cherry, Zhuan Ye
    Pages 5-48

  4. The Second Main Theorem via Negative Curvature

    • William Cherry, Zhuan Ye
    Pages 49-88

  5. Logarithmic Derivatives

    • William Cherry, Zhuan Ye
    Pages 89-106

  6. The Second Main Theorem via Logarithmic Derivatives

    • William Cherry, Zhuan Ye
    Pages 107-117

  7. Some Applications

    • William Cherry, Zhuan Ye
    Pages 119-150

  8. A Further Digression into Number Theory: Theorems of Roth and Khinchin

    • William Cherry, Zhuan Ye
    Pages 151-160

  9. More on the Error Term

    • William Cherry, Zhuan Ye
    Pages 161-186

  10. Back Matter

    Pages 187-203
    Download chapter PDF
Back to top

Keywords

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 allmajor 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)

Authors and Affiliations

  • Department of Mathematics, University of North Texas, Denton, USA

    William Cherry

  • Department of Mathematical Sciences, Northern Illinois University, DeKalb, USA

    Zhuan Ye

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: https://doi.org/10.1007/978-3-662-12590-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2001

  • Hardcover ISBN: 978-3-540-66416-1Published: 24 April 2001

  • Softcover ISBN: 978-3-642-08568-0Published: 04 December 2010

  • eBook ISBN: 978-3-662-12590-8Published: 14 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XII, 203

  • Topics: Functions of a Complex Variable, Several Complex Variables and Analytic Spaces, Number Theory

Publish with us

Policies and ethics

Back to top

Search

Navigation