## 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

### Keywords:

Nevanlinna theory; p-adic functions

Zbl 0645.00003