P-adic Analytic Functions describes the definition and properties
of p-adic analytic and meromorphic functions in a complete
algebraically closed ultrametric field.Various properties of p-adic
exponential-polynomials are examined, such as the Hermite-Lindemann
theorem in a p-adic field, with a new proof. The order and type of
growth for analytic functions are studied, in the whole field and
inside an open disk. P-adic meromorphic functions are studied, not
only on the whole field but also in an open disk and on the
complemental of an open disk, using Motzkin meromorphic products.
Finally, the p-adic Nevanlinna theory is widely explained, with
various applications. Small functions are introduced with results
of uniqueness for meromorphic functions. The question of whether
the ring of analytic functions-in the whole field or inside an open
disk-is a Bezout ring is also examined.
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