Applications of the principle of partitioning of meromorphic functions. II: Accumulations of \(a\)-points and Littlewood property (Q1278920)

Let \(M\) be the class of meromorphic functions in \(C\) that map the upper half-plane to itself. For such a function \(w\) let \(A(r)\) denote the spherical area of the image under \(w\) of the disc \(D(0,r)\) divided by the area of the Riemann sphere. Then the counting function \(n(r,0)\) of zero satisfies \(n(r,0)= A(r)+o(A(r))\) as \(r\to\infty\) outside an exceptional set and similarly for the counting function of the poles. According to the authors' abstract it is shown that there exist classes of meromorphic functions (in \(M)\) whose \(a\)-points mainly occur in arbitrarily small sets, while the spherical derivatives at these points are arbitrarily big. The technical statements of these results involve notations of the first author's paper in [J. Contemp. Math. Anal., Armen. Acad. Sci. 32, No. 3, 2-45 (1997; Zbl 0905.30029)].