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GH from MO
GH from MO
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We consider the Euler product formula $$\sum \frac{1}{n^s}=\prod_p \frac{1}{1-p^s}$$$$\sum_{n=1}^\infty \frac{1}{n^s}=\prod_p \frac{1}{1-p^{-s}}$$

I have two questions about this equality:

1)Does the rate of convergence of each side depend on $s$?

2)For given $s$ is the rate of convergence of the left hand side equal to the rate of convergence of the right hand side of the equality?

We consider the Euler product formula $$\sum \frac{1}{n^s}=\prod_p \frac{1}{1-p^s}$$

I have two questions about this equality:

1)Does the rate of convergence of each side depend on $s$?

2)For given $s$ is the rate of convergence of the left hand side equal to the rate of convergence of the right hand side of the equality?

We consider the Euler product formula $$\sum_{n=1}^\infty \frac{1}{n^s}=\prod_p \frac{1}{1-p^{-s}}$$

I have two questions about this equality:

1)Does the rate of convergence of each side depend on $s$?

2)For given $s$ is the rate of convergence of the left hand side equal to the rate of convergence of the right hand side of the equality?

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Ali Taghavi
Ali Taghavi
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Rate of convergence of the Riemann zeta function and the Euler product formula

We consider the Euler product formula $$\sum \frac{1}{n^s}=\prod_p \frac{1}{1-p^s}$$

I have two questions about this equality:

1)Does the rate of convergence of each side depend on $s$?

2)For given $s$ is the rate of convergence of the left hand side equal to the rate of convergence of the right hand side of the equality?