Value Distribution Theory.

Lo, Yang:

ISBN 10: 3540543791 / ISBN 13: 9783540543794

Editore: Springer : Berlin; Science Press : Beijing,, 1993

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xii, 268 S. Einband mit leichten Lagerspuren, sonst sehr gut erhalten. Sieht ungelesen aus. Sprache: Englisch Gewicht in Gramm: 590.

Codice articolo 74542

Dati bibliografici

• Titolo: Value Distribution Theory.
• Editore: Springer : Berlin; Science Press : Beijing,
• Data di pubblicazione: 1993
• Lingua: Inglese
• ISBN 10: 3540543791
• ISBN 13: 9783540543794
• Rilegatura: 8°, gebundene Ausgabe, Leinen
• Edizione: Auflage: 1.
• Peso: 590 grammi
• Cataloghi dei venditori:
  • Mathematik

Descrizione articolo

Riassunto

It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep- tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 (0) satisfies -1' logn(r, J = a) \ 1m = 1\ r->oo logr for every finite complex value a, with at most one exception. This result, generally known as the Picard-Borel theorem, lay the foundation for the theory of value distribution and since then has been the source of many research papers on this subject.

Contenuti

1 Essentials of Nevanlinna Theory.- 2 Normal Families.- 3 Borel Directions.- 4 Value Distribution of Meromorphic Functions Together with Their Derivatives.- 5 Recent Studies on Borel Directions.- 6 Deficient Values and Borel Directions of Meromorphic Functions.- 7 The Spread Relation and Its Applications.