Value Distribution in p-adic Analysis

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Number Theory
Cover of the book Value Distribution in p-adic Analysis by Alain Escassut, World Scientific Publishing Company
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Author: Alain Escassut ISBN: 9789814730129
Publisher: World Scientific Publishing Company Publication: November 27, 2015
Imprint: WSPC Language: English
Author: Alain Escassut
ISBN: 9789814730129
Publisher: World Scientific Publishing Company
Publication: November 27, 2015
Imprint: WSPC
Language: English

The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation.

Contents:

  • Ultrametric Fields
  • Hensel Lemma
  • Spherically Complete Extensions
  • Analytic Elements
  • Power and Laurent Series
  • Factorization of Analytic Elements
  • Derivative of Analytic Elements
  • Vanishing along a Monotonous Filter
  • Maximum Principle
  • Quasi-Invertible Analytic Elements
  • Meromorphic Functions
  • The Corona Problem on Ab(d(0,1‾))
  • Applications to Curves
  • Growth of the Derivative of an Entire Function
  • Rational Decomposition for Entire Functions
  • and other papers

Readership: Graduate students and researchers interested in p-adic analysis.

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The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation.

Contents:

Readership: Graduate students and researchers interested in p-adic analysis.

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