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How to find the convergence domain of $$\prod(1-\frac{1}{n^z})$$ where $n \ge 2$?

I found that it converges absolutely for $\Re(z)>1$, does not converge for real number $x \leq 1$. (I used $\sum \frac{1}{n^x}$ for these.) But what's it about other points?

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@joriki yes, the definition is the convergence to nonzero. – Gobi Nov 11 '12 at 16:18
Sorry, you're right, I wasn't aware of that definition. – joriki Nov 11 '12 at 16:29

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