Five conjectures, formulated by B. Riemann (1876), concerning the distribution of the non-trivial zeros of the zeta-function , and the expression via these zeros of the number of prime numbers not exceeding a real number . One of the Riemann hypotheses has neither been proved nor disproved: All non-trivial zeros of the zeta-function lie on the straight line .

For the list of all 5 conjectures see Zeta-function.

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