zeta(3), Euler's product formula variation

camilus

the villain with x-ray glasses
Registered Senior Member
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 6309I need help understanding this equality:

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


Any help is greatly appreciated!!!
 
Back
Top