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

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 ??????