This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
\sum_{n=1}^{\infty} \frac{1}{n^s} $$
The image displays the definition of the Riemann zeta function.
The Riemann zeta function, denoted by , is a function of a complex variable that plays a pivotal role in analytic number theory. It is defined by the infinite series: This series converges for complex numbers with real part . The function can be extended to a meromorphic function on the entire complex plane via analytic continuation, with a simple pole at .
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The image displays the definition of the Riemann zeta function. The Riemann zeta function, denoted by (s), is a function of a complex variable s that plays a pivotal role in analytic number theory.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.