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
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from World Scientific Publishing Company

Cover of the book Discovery of the Higgs Boson by Alain Escassut
Cover of the book Surgical Talk by Alain Escassut
Cover of the book Energy from the Nucleus by Alain Escassut
Cover of the book An Elementary Course on the Continuum Theory for Nematic Liquid Crystals by Alain Escassut
Cover of the book 2015 Estimation of Agricultural Productivity and Annual Update of Competitiveness Analysis for Greater China by Alain Escassut
Cover of the book Luminous Pursuit by Alain Escassut
Cover of the book A Course in Analysis by Alain Escassut
Cover of the book The Economics of Small Business by Alain Escassut
Cover of the book Beyond the Moon by Alain Escassut
Cover of the book Singapore Perspectives 2013 by Alain Escassut
Cover of the book Wisdom of the Martians of Science by Alain Escassut
Cover of the book Theory and Practice of Computation by Alain Escassut
Cover of the book A Dynamic Use of Survey Data and High Frequency Model Forecasting by Alain Escassut
Cover of the book Cardioprotective Natural Products by Alain Escassut
Cover of the book History and Philosophy of Biology by Alain Escassut
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy