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The '''Riemann Zeta function''', commonly denoted <math>/zeta(s)</math> is a function that is very important function in number theory. The function can be defined as <math>\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s} </math> when s has a real part greater than 1. The function can then be analytically continued for everywhere where s is non-one (the function has a simple pole at <math>s=1</math>). The function was investigated by a number of mathematicians including Euler who showed that <math>\zeta(2) = \frac{\Pi^2}{6}</math> but was first extensively investigated by [[Bernhard Riemann]] who showed that the behavior of the function was intimately connected to the distribution of [[prime number|prime numbers]]. In particular, where the function is zero is related very closely to the error term of the [[Prime Number Theorem]]. The [[Riemann hypothesis]] is an unsolved conjecture that describes strong restrictions on the locations of the zeros.
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