Gap orders of meromorphic functions on Riemann surfaces.
We examine the boundary behaviour of the generic power series with coefficients chosen from a fixed bounded set in the sense of Baire category. Notably, we prove that for any open subset of the unit disk with a nonreal boundary point on the unit circle, is a dense set of . As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given....
We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.