Abstract:

The main purpose of this paper is to give the covering surface inequality for the meromorphic function on the ring, which studies the problem on ring sequence and promotes the classic Picard theorem. Furtherly, we use Valiron type function to obtain the Borel theorem for the finite positive meromorphic function on the infinite ring sequence.

Key words: Ring, Covering surface, Meromorphic function, Picard theorem, Borel theorem