riemann's zeros

[magicdice]

so i'm plotting the "i" on the y-axis and the real number on the x-axis, right?

and my primes are being generated by the sums of the sine & cosine curves which are related how exactly to my zeros?

and (1/2, y) is a prime for some values of y, but which and how do i work out which?

[seal!]

my point exactly.

[magicdice]

oh, thank you(!)

that was inspirationally useful

[morg_monster]

magicdice I think that may be beyond the scope of many answerbankers...! no offence to them!  I got a first in my MMath degree and firstly i don't think i could answer that and secondly even if i could i couldn't be bothered to go look thru my notes and find out and then type it up... anyway i'm more of a stats person. sorry!

[Marsh]

The extract below from http://www.coolissues.com/mathematics/Riemann/riemann.ht m
lost all of the equations, (written in pink Greek letters) when I pasted it into the answer square.  However, the zeros appear to "lie in the strip of the s-plane for which x is between 0 and 1 inclusive".  Even the bits in English are all Greek to me but you might like to take a look.

Introduction

The famous conjecture known as Riemann' s hypothesis1 is to classical analysis what Fermat's last theorem is to arithmetic. Euler (1737) noted that the formula
  
the sum extending to all positive integers n, and the product to all positive primes p. The necessary conditions of convergence hold for complex values of s with real part >1. Considering  as a function of  of the complex variable s, Riemann (1859) proved that  satisfies a functional equation
   =   
which led Riemann to the theorem that all the zeros of  , except those at s=-2,-4,-6, . . . , lie in the strip of the s-plane for which  where x is the real part of s. Riemann conjectured that all the zeros in the strip should lie on the line x= �. Attempts to prove or disprove this conjecture have generated a vast and intricate department of analysis, especially since Hardy (1914) proved that  has an infinity of zeros on x= � .2 The question is still open in 2000. A prize is available to prove or disprove Riemann's hypothesis.3

[magicdice]

thanks for answers morg_monster and marsh, had a bit of a eureka moment just a minute ago - amazing the wonders a few shots of tequila on a school-night can do for mathematical ponderings(!) - but i get it now:

the z-axis is where i'm plotting my zeta-function outputs, and i'm finding the cumulative total of primes up to N using Gauss's method plus Riemann's refinements (which incorporates my sinusoidal output curve), and the zeros are the factor that defines the rest of the landscape and my last question makes absolutely no sense, i can't have an imaginary prime in any real sense of the word (no pun intended). and on second glance, why the **** would i be adding my sine & cosine curves?!?!?! that'd just be moronic. yaaaaaaay i'm all ready to talk about this in my interview now woooooooo!!!!!!! *wishes someone else gave a **** about this*

[bernardo]

I did A Level maths and you lost me after the first sentence of the question :-(