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#### mathworker

##### Well-known member

- May 31, 2013

- 119

In an article it is given that,

[HR][/HR]

$\zeta(s)$ 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?

[HR][/HR]

\(\displaystyle \zeta(s)=\text{exp}

(\sum_{n=1}^\infty\frac{\Lambda{(n)}}{\text{log}(n)}n^{-s})\)

[HR][/HR](\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 \(\displaystyle s=\rho\)

what are those several $\rho$'s?

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