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On p-adic Nevanlinna theory. (English) Zbl 0673.30035

Complex analysis, Proc. 13th Rolf Nevanlinna-Colloq., Joensuu/Finl. 1987, Lect. Notes math. 1351, 146-158 (1988).
[For the entire collection see Zbl 0645.00003.]
Nevanlinna theory has two central theorems concerning the value distribution of a meromorphic function in one variable. In this paper p- adic analogues of the two theorems for meromorphic functions on \(\{z\in {\mathbb{C}}_ p|\) \(| z| <1\}\) are given. It seems that the formulas, in particular the definition of Nevanlinna’s characteristic function, are more or less copies of the complex case. The meaning of the two p-adic theorems is not made clear in the paper. The only ingredient in the proofs is the well-known Newton-polygon of a meromorphic function.
Reviewer: M.van der Put

MSC:

30G06 Non-Archimedean function theory
12J10 Valued fields
12J15 Ordered fields

Citations:

Zbl 0645.00003