Ahmed Sebbar: Some problems of analytic continuation

We discuss the analytic continuation problem of the series ∑ φ(n)z^n in terms of the analytic properties of the function φ. We apply this procedure to the two series

∑ z^n/n^s,   ∑ (μ(n)/n^s) z^n

(where μ denotes the Möbius function), and we discuss the problems which arise.