Talk:Riemann Xi function

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This article incorporates material from PlanetMath, which is licensed under the GFDL.

[edit] Planet Math errors

The planet-math article implies that

The upper-case Ξ function is defined as
" \Xi(s) = \pi^{-\frac{s}{2}} \Gamma\left(\frac{s}{2}\right) \zeta(s)
although Riemann himself used the notation of a lower case xi (ξ) for this expression. The famous Riemann Hypothesis is equivalent to the assertion that all the zeros of Ξ are real, in fact Riemann himself presented his original hypothesis in terms of that function.

However, this is in direct conflict with mathworld, amnd mathworld appears to be more correct, in saying Xi(t) = ξ(1 / 2 + it) or something like that. This text should be fixed at mathworld, and fixe here. linas 20:56, 2 June 2006 (UTC)

This article is concerned with the lowercase xi function, but it is named using the upper case Xi. Either this article should say anything about Xi, or it should be moved to the name with lowercase xi. Oleg Alexandrov (talk) 23:42, 3 June 2006 (UTC)