Bulletin of the
Korean Mathematical Society BKMS

In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the $p$-Casorati determinant with $p\in\mathbb C^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition ``order=0". The results obtained include $p$-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.

Keywords: second main theorem, Nevanlinna theory, Casorati determinant, zero-order meromorphic mapping, hyperplanes

MSC numbers: Primary 53A10; Secondary 53C42, 30D35, 32H30