The expression ζ(s) = 1 + 1/2s + 1/3s + 1/4s + ... is the definition of the Riemann zeta function. This function is defined for complex values of s with real part greater than 1, and it is extended to the whole complex plane using analytic continuation.
The Riemann zeta function is an important object in number theory and has connections to many other areas of mathematics, including complex analysis, algebraic geometry, and probability theory.
One of the most famous and important properties of the Riemann zeta function is the Riemann Hypothesis, which states that all non-trivial zeros of the zeta function lie on the critical line with real part equal to 1/2. The Riemann Hypothesis is one of the most famous unsolved problems in mathematics and has been the subject of intense study for over a century.
Despite its importance and the many partial results that have been obtained, the Riemann Hypothesis remains unsolved, and its proof or disproof would have far-reaching implications for number theory and many other areas of mathematics.
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