Riemann

(Another of the Prime Pages' resources)

David R. Wilkins School of Mathematics Trinity College, Dublin

Wikipedia, the free encyclopedia.

In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics; i.e. a choice of positive-definite quadratic form on a manifold's tangent spaces which varies smoothly from point to point.

Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 - 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function ?z(s)? called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation z(s) = 0 lie on a straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.

From Wikipedia, the free encyclopedia.

Jonathan Borwein and Kwok-Kwong Stephen Choi [Retrieve PostScript]

Ingrid Picquenot et Jean-Francois Viaud

memoire de maitrise a l'universite de La Rochelle

17 septembre 1826, - 20 juillet 1866

(Xavier Hubaut)

(Mathematicians - University of St Andrews, Scotland)

Contents of Volume 1, Number 7 bulletin of the american Mathematical Society 1895