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.
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