Hey guys, while studying dirichlet series I came along a theorem stating that every D.S. has a convergence abscissa (possibly +Infinity). Now there was a corollary stating that any Ordinary D.S. $\displaystyle \sum_{n=1}^{\infty} a_n/n^s$ has a absolute convergence abscissa, which doesn't differ by more than 1 from the normal abscissa, but there is no proof. Can anyone prove this?