Singularities: Singularities (in complex function theory) refer to points in the complex plane where the function is not analytic (analytic at a point means it can be represented by a power series convergent in a neighborhood of the point). A pole is a singularity, where the function can be represented by a power series plus a finite series of inverse powers at that point. A simple pole (from what I remember) means that there is only one inverse term of the form c/(z-a), where a is the location of the pole.

The convergence question refers to the series representation of the zeta function. There is a process called analytic continuation, which allows the definition to be extended to all points in the z plane, which are not singularities.

• Some Answers - petersand - August 30, 2001 - 22:33 UTC
  • Dear Peter - mathman - August 31, 2001 - 02:26 UTC
  • You are the manifest.. - bruce - August 31, 2001 - 05:37 UTC
    • That was meant for Peter.. - bruce - August 31, 2001 - 05:39 UTC
    • Manifest - petersand - September 1, 2001 - 18:43 UTC
• Thanx.....nt - smartguy - August 31, 2001 - 00:22 UTC