Nevanlinna’s Theory of Value Distribution: The Second Main Theorem and its Error TermsSpringer Science & Business Media, 14 mar 2013 - 203 pagine 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. |
Sommario
The Second Main Theorem via Negative Curvature | 49 |
Logarithmic Derivatives | 89 |
The Second Main Theorem via Logarithmic Derivatives | 107 |
Some Applications | 119 |
Theorems of Roth | 151 |
More on the Error Term | 161 |
Bibliography | 187 |
Glossary of Notation | 193 |
Altre edizioni - Visualizza tutto
Nevanlinna’s Theory of Value Distribution: The Second Main Theorem and its ... William Cherry,Zhuan Ye Anteprima limitata - 2001 |
Nevanlinna’s Theory of Value Distribution: The Second Main Theorem and its ... William Cherry,Zhuan Ye Anteprima non disponibile - 2010 |
Parole e frasi comuni
absolute value Ahlf Ahlfors aj,r apply assume b₁ bound Cfmt Chapter characteristic function constant continuous function Corollary counting function curvature denote Diophantine approximation distinct points entire function equation error term exceptional set f'(reio finite func function f function on D(R Fundamental Theorem geometric growth lemma hence holomorphic function inequality integral Jensen Formula Khinchin function Let a1 Let f lim inf lim sup log ƒ log log log T(f log T(f,r log+ Logarithmic Derivative logr Math meromorphic function multiplicity Nev(R Nevanlinna functions Nevanlinna theory non-constant meromorphic function nondecreasing notation Note Nram f number field number theory Picard's Theorem points in P¹ Poisson kernel polynomial precise proof of Theorem Proposition radii Ramification Theorem rational functions Re¹º reader reio Remark Riemann Riemann sphere Roth's Theorem Second Main Theorem sufficiently large Theorem of Algebra zeros