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An improvement of the \(p\)-adic Nevanlinna theory and application to meromorphic functions. (English) Zbl 0937.30028
Kąkol, J. (ed.) et al., \(p\)-adic functional analysis. Proceedings of the 5th international conference in Poznań, Poland, June 1-5, 1998. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 207, 29-38 (1999).
Author’s summary: In this article we give an improvement of the ultrametric Nevanlinna theory and apply these results to a problem of uniqueness for ultrametric meromorphic functions. We obtain a new construction of bi-urs’ of \(n\) elements for such functions for every \(n\geq 5\). In particular we find bi-urs’ of the form \((S_n,\{\infty\})\) where \(S_n\) is the set of the zeros of the polynomial \(R_n(x)= {(n-1)(n-2) \over 2}x^n-n(n-2) x^{n-1}+ {n(n-1) \over 2} x^{n-2} -c\) with \(n\geq 5\).
For the entire collection see [Zbl 0919.00056].

MSC:
30G06 Non-Archimedean function theory
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