riemann zeta functionpole question?


by lostcauses10x
Tags: functionpole, riemann, zeta
lostcauses10x
lostcauses10x is offline
#1
Oct20-11, 09:04 PM
P: 94
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??
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camilus
camilus is offline
#2
Oct25-11, 04:29 PM
P: 150
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
lostcauses10x is offline
#3
Oct25-11, 05:09 PM
P: 94
Quote Quote by camilus View Post
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 ??????


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