Difference between revisions of "Riemann hypothesis"

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The '''Riemann hypothesis''' states that the non-trivial zeros of the [[Riemann Zeta function]] function all have real component <math>\frac{1}{2}</math>. The conjecture was first proposed by [[Bernhard Riemann]] in 1859 and is considered to be the greatest unsolved problem in mathematics. The hypothesis was listed as one of the seven [[Millennium problems]] by the Clay Mathematics Institute and there is a million dollar prize for its solution.<ref>http://www.claymath.org/millennium/</ref> The statement is essentially equivalent to the claim that the error term in the [[pime number theorem]] is small. Alternatively, the Riemann hypothesis can be thought of as a statement that the [[prime number]]s are very smoothly distributed.   
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The '''Riemann hypothesis''' states that the non-trivial zeros of the [[Riemann Zeta function]] function all have real component <math>\frac{1}{2}</math>. The conjecture was first proposed by [[Bernhard Riemann]] in 1859 and is considered to be one of the greatest unsolved problem in mathematics. The hypothesis is one of [[Hilber]]'s twenty-three problems and  was listed as one of the seven [[Millennium problems]] by the Clay Mathematics Institute. There is a million dollar prize for its solution.<ref>http://www.claymath.org/millennium/</ref> The statement is essentially equivalent to the claim that the error term in the [[prime number theorem]] is small. Alternatively, the Riemann hypothesis can be thought of as a statement that the [[prime number]]s are very smoothly distributed.   
  
 
==References==
 
==References==
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[[Category:Complex analysis]]
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Revision as of 15:15, 22 July 2018

The Riemann hypothesis states that the non-trivial zeros of the Riemann Zeta function function all have real component . The conjecture was first proposed by Bernhard Riemann in 1859 and is considered to be one of the greatest unsolved problem in mathematics. The hypothesis is one of Hilber's twenty-three problems and was listed as one of the seven Millennium problems by the Clay Mathematics Institute. There is a million dollar prize for its solution.[1] The statement is essentially equivalent to the claim that the error term in the prime number theorem is small. Alternatively, the Riemann hypothesis can be thought of as a statement that the prime numbers are very smoothly distributed.

References

  1. http://www.claymath.org/millennium/
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