What is the abscissa of convergence of the series $\sum\limits_{n=1}^{\infty} (-1)^n \frac {1} {n^s}\ $?
In the lecture note our instructor claimed that the abscissa of convergence of the above series is $0.$ It is a well-known fact that the abscissa of convergence of the zeta function is $1$ and hence the abscissa of absolute convergence of the alternating zeta function is also equal to $1.$ But I don't have any idea about it's abscissa of convergence. Is there any result related to that?
Any help in this regard would be much appreciated. Thanks for investing your valuable time in reading my question.