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