Riemann HypothesisWikipedia Reference InformationIn mathematics, the Riemann hypothesis (also called the Riemann zetahypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous, and important, 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 (RH) is a conjecture about the distribution of the zeros of the Riemann zetafunction ?(s). The Riemann zetafunction 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 nontrivial zeros, and states that: The real part of any nontrivial zero of the Riemann zeta function is ½. Thus the nontrivial zeros should lie on the socalled critical line ½ + it with t a real number and i the imaginary unit. The Riemann zetafunction along the critical line is sometimes studied in terms of the Zfunction, whose real zeros correspond to the zeros of the zetafunction on the critical line. 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, mainly because a large number of deep and important other results have been proven under the condition that it holds. 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). A $1,000,000 prize has been offered by the Clay Mathematics Institute for the first correct proof. The complete, uptodate and editable article about Riemann Hypothesis can be found at Wikipedia: Riemann Hypothesis http://en.wikipedia.org/wiki/Riemann_Hypothesis

