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Jul 18, 2017 at 11:57 comment added reuns see what I wrote
Jul 18, 2017 at 11:37 comment added GH from MO @reuns: I don't think so, because $H(s)$ diverges at $s=3/2$. Perhaps, with a more refined argument, one can get meromorphic continuation to $\Re(s)>1$, but even then it is unclear why $\Re(s)=1$ is a natural boundary. Feel free to add your more detailed analysis (in a separate post).
Jul 18, 2017 at 11:29 comment added reuns With the same argument you get the analytic continuation to $\Re(s) > 1$ and a natural boundary there
Jul 18, 2017 at 11:02 vote accept CommunityBot
Jul 19, 2017 at 7:34
Jul 18, 2017 at 10:56 history edited GH from MO CC BY-SA 3.0
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Jul 18, 2017 at 10:49 history answered GH from MO CC BY-SA 3.0