Riemann zeta functionpole question?

[lostcauses10x]

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??

 

[camilus]

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

 

[lostcauses10x]

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

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 ?