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Zeta Function -1 1/2 and prime numbers

  1. Jan 26, 2014 #1
    I talked with an old friend of mine. We discussed prime numbers and Ulams Spiral, and the mathematical patterns that surround us all. He brought up something called the Zeta-Function and something about -1 1/2 and how this all related to prime numbers. I did a google search and found some interesting results but didn't quite find enough on the purpose of -1 1/2, guess I should have dug a little deeper. Anyways could someone please explain the Zeta Function and why it is important and purposeful, as well as it's correlation to prime numbers and -1 1/2.

    Thank You
     
  2. jcsd
  3. Jan 27, 2014 #2

    mathman

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    I don't know where -1 1/2 comes from. There is a famous open question in mathematics (called the Riemann hypothesis) which says that in the strip in the complex plane (0<x<1, where x is the real part of z) the only zeroes of the zeta function are along the line x = 1/2.

    Start here:
    http://en.wikipedia.org/wiki/Riemann_zeta_function
     
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