On differential polynomials of algebroid functions (Q2744410)

This paper is devoted to proving the following theorem: Let \(w(z)\) be a \(\nu\)-valued algebroid function in the complex plane, and \(p(w)\) be a differential polynomial in \(w\) and its derivatives with meromorphic coefficients. Then \(p(w(z))\) is a \(\lambda\)-valued algebroid function such that for some \(k\in\mathbf N\), \(\lambda k=\nu\). The last equality is the novelty here as it is well-known that \(p(w(z))\) is algebroid with \(\lambda\leqq\nu\). Unfortunately, several misprints and partially confusing notations disturb in reading of the paper.