Limit involving the zeta function.

Calculus Level 3

The zeta function is a function of complex argument defined as: \[\zeta(s):=\sum_{n=1}^\infty \dfrac1{n^s}.\] What is the following limit equal to? \[\lim\limits_{s\to\infty}\dfrac{\zeta(\pi^s)}{\zeta(s\ln s)}.\]

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