Some applications of p-adic Nevanlinna theory (Q1175289)

The author studies the \(p\)-adic analogue of the ``Nevanlinna theory'' introduced by \textit{Hà Huy Khoái} [Duke Math. J. 50, 695-711 (1983; Zbl 0544.30039)]. By slightly modifying the definition of the characteristic function \(T\) introduced by the latter --- in fact, by following the definition of his complex model more faithfully --- the author obtains the \(p\)-adic analogues of the two fundamental theorems of Nevanlinna theory. He then gives some classical applications to meromorphic functions. Note that \textit{A. Boutabaa} has independently obtained some similar results [Manuscripta Math. 67, No. 3, 251-269 (1990; Zbl 0697.30047)] and some applications to a \(p\)-adic analogue of the Malmquist-Yosida theorem (if \((dy/dx)^ m=R(x,y)\) has no nonrational meromorphic solutions in the whole of \(\mathbb{C}_ p\), with \(R(x,y)\in\mathbb{C}_ p(x,y)\), then \(R(x,y)\) is in \(\mathbb{C}_ p[y](x)\) and has degree less than \(2m\) in \(y\)).