Uniqueness theorems in an angular domain

Meromorphic functions in the unit disc that share values in an angular domain

“…Zheng firstly took into account the uniqueness of meromorphic functions sharing values in an angular domain and extended fivevalue theorem and four-value theorem in the complex plane to an angular domain (see [5,6]). Since then, the uniqueness of meromorphic functions in an angular domain attracted many investigations (see [7][8][9], etc.). In fact, he proved the following theorems on the basis of the relation between the Pólya peaks and deficiencies of meromorphic functions.…”

“…In this paper, we adopt a proof method which is different from that of [5][6][7][8][9], and obtain Theorem 1.1. Let f (z) and g(z) be two meromorphic functions in D 1 , a j ∈ C ∞ ( j = 1, 2, .…”

“…In the proof of theorems in [5][6][7][8][9], Nevanlinna theory in an angular domain plays a key role (see [10]). In this paper, we adopt a proof method which is different from that of [5][6][7][8][9], and obtain Theorem 1.1.…”

Nevanlinna’s Five Values Theorem on Annuli

“…Zhang, T.B. Cao and W.C. Lin (including [12][13][14][15][16]) considered many uniqueness problem on meromorphic functions on the angular domain.…”

On the uniqueness of meromorphic functions that share four values in one angular domain

“…values in some angular domains of C. It is an interesting topic to investigate the uniqueness with shared values in the remaining part of the complex plane removing an unbounded closed set, see [14,15,1,9,7,11]. In [15], Zheng continued to investigate this subject.…”