zeta(3), Euler's product formula variation

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

  1. 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 6309 I 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!!!

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