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