From Wikipedia.org: 'Georg Friedrich Bernhard Riemann (September 17, 1826 - July 20, 1866) (pronounced REE mahn or in IPA ['ri:man]) was a German mathematician who made important contributions to analysis and differential geometry, some of them paving the way for the later development of general relativity.
In mathematics, the Riemann hypothesis (also called the Riemann zeta-hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous unsolved problems. It has been an open question for well over a century, despite attracting concentrated efforts from many outstanding mathematicians. Unlike some other celebrated problems, it is more attractive to professionals in the field than to amateurs.
The Riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta-function ζ(s). The Riemann zeta-function is defined for all complex numbers s ≠ 1. It has zeros at the negative even integers (i.e. at s = −2, s = −4, s = −6, ...). These are called the trivial zeros. The Riemann hypothesis is concerned with the non-trivial zeros, and states that:
The real part of any non-trivial zero of the Riemann zeta function is ½.
Thus the non-trivial zeros should lie on the so-called critical line ½ + it with t a real number and i the imaginary unit. The Riemann zeta-function along the critical line is sometimes studied in terms of the Z-function, whose real zeros correspond to the zeros of the zeta-function on the critical line.
The real part (red) and imaginary part (blue) of the critical line Re(s) = 1/2 of the Riemann zeta-function. You can see the first non-trivial zeros at Im(s) = ±14.135, ±21.022 and ±25.011.
A polar graph of zeta, that is, Re(zeta) vs. Im(zeta), along the critical line s=it+1/2, with t running from 0 to 34The Riemann hypothesis is one of the most important open problems of contemporary mathematics; a $1,000,000 prize has been offered by the Clay Mathematics Institute for a proof. Most mathematicians believe the Riemann hypothesis to be true. (J. E. Littlewood and Atle Selberg have been reported as skeptical. Selberg's skepticism, if any, waned, from his young days. In a 1989 paper, he suggested that an analogue should hold for a much wider class of functions, the Selberg class.)'
2006-06-19 01:16:20
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answer #1
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answered by Sherry K 5
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Aribert Reimann (born 4 March 1936) is an German opera composer and pianist. His version of Lear was written at the suggestion of Dietrich Fischer-Dieskau who sang the title role.
2006-06-19 01:10:59
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answer #2
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answered by Anry 7
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