Back to AtD Zeta functions

[Prashant Kumar]

First we're gonna need complex numbers, made of a real part (normal
numbers) plus an imaginary part. Imaginary numbers are defined by multiples
of *i*=squareroot(-1). Imagine a 2D graph, the vertical axis marked with
multiples of *i* and the horizontal axis with real numbers. So on this 2D
graph we can define a complex number as a point. Call such a point s =
\sigma + \rho, \sigma and \rho being real and imaginary numbers resp.

Since it takes real and imaginary inputs, and we plot the output in the
third dimension, the Riemann Zeta function can be visualised as a surface
sitting above the complex number graph; that's what you saw, Mark (see here
http://en.wikipedia.org/wiki/Riemann_zeta_function for the same thing with
magnitude represented as colour).  If I have a RZ function, writing R as a
function of s as R(s), the zeroes are the values of s for which R(s)=0.
 The Riemann Hypothesis (unproven) states that the zeroes of the RZ
function have real part 1/2. Formally, R(1/2 + \rho) = 0. This gives you a
line on the surface of the RZ function (known as the critical line) along
which the zeroes are hypothesised to lie. That wasn't too bad, right?

Verifying this hypothesis is notoriously hard.

On 15 July 2012 21:27, Mark Kohut <markekohut at yahoo.com> wrote:

> "Except that this one's horizontal and drawn on a grid of latitude and
> longitude,
> instead of rel vs imaginary values---where Riemann said that all the
> zeroes of the
> Beta function will be found."
>
> p. 937 Don't know enough math to have a feel for Zeta functions but
> Wolfram's
> maths guide online shows Beta functions kinda graphed in three dimensions,
> with raised sections, waves, folds etc....
>
> And all I can associate at the moment are the raised maps, showing land
> formations,
> and the phrase
>
> History is a step-function.
>
> Anyone, anyone? Bueller?
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://waste.org/pipermail/pynchon-l/attachments/20120715/778668c8/attachment.html>