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Nevanlinna's Theory of Value Distribution

  • Kartonierter Einband
  • 220 Seiten
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This monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution as well as a valuable referenc... Weiterlesen
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This monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution as well as a valuable reference for research specialists. 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.

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)

1. The First Main Theorem.- 2. The Second Main Theorem via Negative Curvature.- 3. Logarithmic Derivatives.- 4. The Second Main Theorem via Logarithmic Derivatives.- 5. Some Applications.- 6. A Further Digression into Number Theory: Theorems of Roth and Khinchin.- 7. More on the Error Term.- Glossary of Notation.


Titel: Nevanlinna's Theory of Value Distribution
Untertitel: The Second Main Theorem and its Error Terms
EAN: 9783642085680
ISBN: 3642085687
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Genre: Mathematik
Anzahl Seiten: 220
Gewicht: 341g
Größe: H235mm x B155mm x T12mm
Jahr: 2010
Auflage: Softcover reprint of hardcover 1st ed. 2001

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