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Riemann zeta function: Riemann zeta function, function useful in number theory for investigating properties of prime numbers. Written as О¶(x), it was originally As readers of Greg Chaitin's article know, it's zeta function time. Mathematicians who read one of the recent popular accounts of the Riemann Hypothesis might be

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The Riemann zeta function satisfies the functional equation (known as the Riemann functional equation or Riemann's functional equation) where О“(s) is the gamma function, which is an equality of meromorphic functions valid on the whole complex plane. This equation relates values of the Riemann zeta function at the points s and 1 в€’ s. The Riemann zeta function and probability theory applications to the study of zeros are probably more anecdotal in terms of the Riemann zeta function

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The Riemann zeta function has some trivial zero points like $-2,-4,-6.$ The hypothesis says that the other zero points lie on the critical line $\Re(s)=\dfrac12$. This hypothesis had many application in analysis and number theory. The first proof of the prime number theorem used this conjecture. The rst applications of zeta functions have been the arithmetic progession tral object of the theory is the Riemann zeta function, de ned for ~~1 by the~~

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