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Riemann zeta functionpole question?

  1. Oct 20, 2011 #1
    The simple pole at on is due to that its value of course is not closed due to it is an infinite value.

    My question is: is this value of infinity, positive or negative. or both??
  2. jcsd
  3. Oct 25, 2011 #2
    positive. The RZF has a pole at s=1 because at s=1 it is equal to the harmonic series sum 1+1/2+1/3+1/4+1/5+...= infinity
  4. Oct 25, 2011 #3
    Thank you:

    So next question is,

    Since say at 1/2 the value of the zeta function is negative. and tends in the negative direction continuing closer you get to one (of course with the limit less than one):and the pole at one is positive, were along the real line is a missing zero????

    Positive value going to a negative value on a line due to a function and no cross over in value at zero ??????
    Last edited: Oct 25, 2011
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