A remark on three-sheeted algebroid surfaces whose Picard constants are five (Q1902056)

The authors study the value distribution of algebroid functions. By the theory of Selberg and Ullrich the number of Picard values of functions on an \(n\)-sheeted Riemann surface \(R\) can be estimated: \(P(R)\leq 2n\). In the present paper the case \(n=3\) is analyzed and for a class of surfaces \(R\) \(P(R) =5\) is proved. A result of Ozawa and the first author is generalized.