Author: Alain Escassut
Publisher: World Scientific
' 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 FieldsHensel LemmaSpherically Complete ExtensionsAnalytic ElementsPower and Laurent SeriesFactorization of Analytic ElementsDerivative of Analytic ElementsVanishing along a Monotonous FilterMaximum PrincipleQuasi-Invertible Analytic ElementsMeromorphic FunctionsThe Corona Problem on Ab(d(0,1‾))Applications to CurvesGrowth of the Derivative of an Entire FunctionRational Decomposition for Entire Functionsand other papers Readership: Graduate students and researchers interested in p-adic analysis. Keywords:p-Adic;Transcendental Numbers;Meromorphic;Nevalinna Theory'