Clay Mathematics Institute. "The Riemann Hypothesis." .
Conrey, J. B. "The Riemann Hypothesis." 50,341-353, 2003. .
According to Fields medalist Enrico Bombieri, "The failure of the Riemann hypothesis would create havoc in the distribution of prime numbers" (Havil 2003, p. 205).
That is the Riemann Hypothesis.
In Ron Howard's 2001 film , John Nash (played by Russell Crowe) is hindered in his attempts to solve the Riemann hypothesis by the medication he is taking to treat his schizophrenia.
The Riemann Hypothesis For Dummies @ Things Of …
The Riemann hypothesis was computationally tested and found to be true for the first zeros by Brent (1982), covering zeros in the region ). S. Wedeniwski used ZetaGrid () to prove that the first trillion () nontrivial zeros lie on the . Gourdon (2004) then used a faster method by Odlyzko and Schönhage to verify that the first ten trillion () nontrivial zeros of the function lie on the . This computation verifies that the Riemann hypothesis is true at least for all less than 2.4 trillion. These results are summarized in the following table, where indicates a .
What does proving the Riemann Hypothesis accomplish?
André Weil proved the Riemann hypothesis to be true for field functions (Weil 1948, Eichler 1966, Ball and Coxeter 1987). In 1974, Levinson (1974ab) showed that at least 1/3 of the must lie on the (Le Lionnais 1983), a result which has since been sharpened to 40% (Vardi 1991, p. 142). It is known that the zeros are symmetrically placed about the line . This follows from the fact that, for all complex numbers ,