| 31. | This estimate is quite close to the conditional result that follows from the Riemann hypothesis.
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| 32. | Vaughan improved this in 1977, showing that, if the generalized Riemann hypothesis is true then
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| 33. | The connection with random unitary matrices could lead to a proof of the Riemann hypothesis.
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| 34. | The last two parts were quite consciously modeled on the Riemann zeta function and Riemann hypothesis.
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| 35. | The value for was originally computed assuming the Riemann hypothesis; it has since been verified unconditionally.
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| 36. | :Among the Millennium Prize Problems the Riemann hypothesis was still completely open as of this morning.
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| 37. | For example, take " Riemann Hypothesis ".
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| 38. | The extended Riemann hypothesis for abelian extension of the rationals is equivalent to the generalized Riemann hypothesis.
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| 39. | If the integers were a curve over a field, the same proof would prove the Riemann hypothesis.
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| 40. | The extended Riemann hypothesis extends the Riemann hypothesis to all Dedekind zeta functions of algebraic number fields.
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