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Channel: What is the analytic continuation of $\varphi(s)=\sum_{n \ge 1} e^{-n^s}?$ - MathOverflow
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What is the analytic continuation of $\varphi(s)=\sum_{n \ge 1} e^{-n^s}?$

My research has lead me to the following function that I'm trying to continue. 3 Months ago I posted this question to MSE, and have placed 3 bounties on the question, but haven't received an answer, so...

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Answer by Caleb Briggs for What is the analytic continuation of...

This is nowhere near a formal answer, but it might contain some useful starting points for doing computation.The problematic aspect of the function$$ \varphi(s) = \Gamma\left(1+\frac{1}{s}\right) +...

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