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20 hours ago vote accept John_zyj
21 hours ago comment added Iosif Pinelis @John_zyj : If your conjectured strict inequality were true for all $\sigma>1$, then the corresponding non-strict inequality would hold in the limit as $\sigma\to\infty$. Anyhow, I have now remarked that the counterexample works for all real $\sigma\ge2.57$.
21 hours ago history edited Iosif Pinelis CC BY-SA 4.0
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21 hours ago history edited Iosif Pinelis CC BY-SA 4.0
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21 hours ago history edited Iosif Pinelis CC BY-SA 4.0
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22 hours ago history answered Iosif Pinelis CC BY-SA 4.0