I have tried to write a program to compute the Zeta function for complex arguments. In particular, I wanted to look at non trivial zeros.
My HP calc and my program agree on some spot checked terms.
For example, 1 / (2 ^ s) where s is equal to (.5 + 14.1347), my program and my HP calculator agree on the answer.
But after adding the first 1000 terms, I don't see any obvious convergence.
How fast does the Zeta function converge? Can you think of any obvious way for me to have made mistakes when adding the terms, or mistakes in my understanding?