In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential opera- tions are closed. On ba...In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential opera- tions are closed. On basis of these works, we firstly prove the Second Main Theorem concerning small algebroid functions for v-valued algebroid functions.展开更多
Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（...Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（z）） = E（aj,M（z）） （j = 1,..., 2v ＋ 2k ＋ 1） holds in the angular domain Ω（θ-δ,θ-δ）, where b, aj （j = 1,..., 2v -b 2k -k 1） are complex constants. The same results axe obtained for the case that△（θ） is a Borel direction of order ∞ （or ρ（τ）） of W（z） （or M（z））.展开更多
基金Supported by National Nature Science Foundation of China (Grant Nos. 10771011, 10871076, 11101096 and 11171013)
文摘In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential opera- tions are closed. On basis of these works, we firstly prove the Second Main Theorem concerning small algebroid functions for v-valued algebroid functions.
基金Supported by the National Natural Science Foundation of China (Grant No. 10471048)the Research Fund of the Doctoral Program of Higher Education (Grant No. 20050574002)
文摘Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（z）） = E（aj,M（z）） （j = 1,..., 2v ＋ 2k ＋ 1） holds in the angular domain Ω（θ-δ,θ-δ）, where b, aj （j = 1,..., 2v -b 2k -k 1） are complex constants. The same results axe obtained for the case that△（θ） is a Borel direction of order ∞ （or ρ（τ）） of W（z） （or M（z））.
