complex power series Definition and 1 Threads

Whether a complex power series ##\sum_{k=0}^\infty c_k (z - z_0)^k## converges at a point ##\tilde z \in \mathbb C## then it converges absolutely in the open disk ##|z−z_0|<|\tilde z−z_0|=r##. Assume now a power series convergent on the circle ##|z−z_0|=r##, does it imply absolute convergence...