Many consider it to be the most important unsolved problem in pure mathematics Bombieri It is of great interest in number theory because it implies results about the distribution of prime numbers. The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture , comprise Hilbert's eighth problem in David Hilbert 's list of 23 unsolved problems ; it is also one of the Clay Mathematics Institute's Millennium Prize Problems. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields. These are called its trivial zeros. However, the negative even integers are not the only values for which the zeta function is zero.

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