# zeta(3), Euler's product formula variation

Discussion in 'Physics & Math' started by camilus, Jun 11, 2013.

1. ### camilusthe villain with x-ray glassesRegistered Senior Member

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View attachment 6308

Hi everyone. I'm trying to understand the step where they wrote

∏1/(1+p^-3) =Ʃ(-1)^ord(k)/k^3

How can I see this? I know the Euler product formula, but it has a negative sign before the p^-3, where here we have a + sign.

Thanks for the help.

View attachment 6309 I need help understanding this equality:

$\prod_{p-prime} \frac{1}{1+\frac{1}{p^3}}= \sum_{k=1}^\infty \frac{(-1)^{\sum_p ord_p(k)}}{k^3}$

Any help is greatly appreciated!!!