New applications of the \(p\)-adic Nevanlinna theory (Q2317190)

The paper consists of two parts. The first one (Sections 1--5) is a concise survey of non-Archimedean Nevanlinna theory. Note that this theory is a well-developed branch of function theory comparable with its classical counterpart; see [the first author, Value distribution in \(p\)-adic analysis. Hackensack, NJ: World Scientific (2016; Zbl 1350.30002)]. The second part (Section 6) contains new results on problems of uniqueness for meromorphic functions having finitely many poles, sharing points or a pair of sets, defined either in the whole algebraically closed field \(K\) of characteristic 0 complete with respect to an ultrametric absolute value, or in an open disk, or in the complement of an open disk.