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!!!
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!!!