I came across the following interesting limit
$$\lim\limits_{n\to\infty}\left(\min(x^{n+1}\zeta(x))-\min(x^{n}\zeta(x))\right)$$ for $x\in\mathbb{R}$ and $x\gt1.$ Calculation highly suggests the solution is $e\log x.$
How can we prove this?
2026-03-25 01:23:55.1774401835
Limit of local minimum of function involving zeta function ($e\log x$)
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