%0 Journal Article
%T On the range of $\sum_{n=1}^\infty\pm c_n$
%A Xinggang He
%A Chuntai Liu
%J Mathematics
%D 2013
%I arXiv
%X Let $\{c_n\}_{n=1}^\infty$ be a sequence of complex numbers. In this paper we answer when the range of $\sum_{n=1}^\infty\pm c_n$ is dense or equal to the complex plane. Some examples are given to explain our results. As its application, we calculate the Hausdorff dimension of the level sets of a Rademacher series with complex coefficients.
%U http://arxiv.org/abs/1309.7745v1