Nevanlinna’s Theory of Value Distribution

The Second Main Theorem and its Error Terms

William Cherry, Zhuan Ye (Autoren)

Buch | Hardcover

XII, 203 Seiten

2001 | 2001
Springer Berlin (Verlag)
978-3-540-66416-1 (ISBN)

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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.

From the contents:
The First Main Theorem
- The Second Main Theorem via Negative Curvature
- Logarithmic Derivatives
- The Second Main Theorem via Logarithmic Derivatives
- Some Applications Chapter
- A Further Digression into Number Theory: Theorems of Roth and Khinchin
- More on the Error Term

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)

Erscheint lt. Verlag	24.4.2001
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XII, 203 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	432 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Schlagworte	11J97 • 30D35 • Approximation • Complex Analysis • diophantine • Diophantine approximation • error terms • Nevanlinna • Nevanlinnasche Theorie • Nevanlinna theory • Number Theory • value distribution
ISBN-10	3-540-66416-5 / 3540664165
ISBN-13	978-3-540-66416-1 / 9783540664161
Zustand	Neuware