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Zero's of zeta function

mathworker

Active member
May 31, 2013
118
In an article it is given that,
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\(\displaystyle \zeta(s)=\text{exp}
(\sum_{n=1}^\infty\frac{\Lambda{(n)}}{\text{log}(n)}n^{-s})\)​
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$\zeta(s)$ has pole at $s=1$ and zeroes at several $s=\rho$.
here i think he considered the function inside the exponential rather than whole exponential to obtain poles and zeroes but I think we should consider it along with exponential or can we?.Or does he consider the entire function if so how does it have pole at s=1 and zeroes at \(\displaystyle s=\rho\)
what are those several $\rho$'s?
 
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