Difference between revisions of "Riemann hypothesis"
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| − | The '''Riemann hypothesis'''... | + | 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 by many to be one of the greatest unsolved problems in mathematics. The problem 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|prime numbers]] are very smoothly distributed. |
==References== | ==References== | ||
Revision as of 18:10, April 17, 2010
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 by many to be one of the greatest unsolved problems in mathematics. The problem was listed as one of the seven Millennium problems by the Clay Mathematics Institute and there is a million dollar prize for its solution.[1] 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 numbers are very smoothly distributed.