Alain Escassut and Jacqueline Ojeda: Unique range sets of 5 points for unbounded analytic functions inside an open disk, p.367-379

Abstract:

Let K be a complete algebraically closed p-adic field of characteristic $p\geq 0$ and let ${\cal A}_u(d(a,R^-))$ be the set of unbounded analytic functions inside the disk $d(a,R^-)=\{x\in \K \ \vert : \vert x-a\vert<R\}$. We recall the definition of urscm and the ultrametric Nevanlinna Theory on $3$ small functions in order to find new urscm for ${\cal A}_u(d(a,R^-))$. Results depend on the characteristic. In characteristic $0$, we can find urscm of $5$ points. Some results on bi-urscm are given for meromorphic functions.

Key Words: p-adic analytic functions, URSCM, Nevanlinna, Ultrametric, Unicity, Distribution of values.

2000 Mathematics Subject Classification: Primary: 12J25;
Secondary: 30D35, 30G06.

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