On the cardinality of unique range sets with weight one - Chakraborty, B.; Chakraborty, S. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
UDC 517.9 Two meromorphic functions f and g are said to share the set SC{∞} with weight lN{0}{∞}, if E_f(S,l)=E_g(S,l), where E_f(S,l)=_a S {(z,t) C×N | f(z)=a with multiplicity p }, where t=p if p≤ l and t=p+1 if p>l. In this paper, we improve and supplement the result of L. W. Liao and C. C. Yang [Indian J. Pure and Appl. Math., 31, No 4, 431–440 (2000)] by showing that there exist a finite set S with 13 elements such that E_f(S,1)=E_g(S,1) implies fg.