[ATTACH] 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...
Thank you.
thats a very knowledgeable response q_wave. I started off doing computer engineering but even then, I could only build up the desire to take...
Im sure of what Im saying, perhaps I wasnt clear enough. The first derived integral after the Mellin inversion and substitutions z->n*n*pi*z and...
okay. At first I thought we were finding the residue of \frac{\xi(s)}{s(s-1)}z^{-s/2} which would be the same as finding the residue of...
do you see the (z^-s/2)/2 in front of the ds on the bottom of page 174? that /2 canceled the 2 in \frac{2\xi(s)}{s(s-1)}. But the negative sign...
actually the factor of 2 is wrong, well not wrong but it was canceled out earlier. And how I said, they took a big O bound so it is irrelevant. But...
t=\frac{s-1/2}{i} plug in s=1/2+i(inf) t=\frac{1/2+i\infty-1/2}{i} = \frac{i \infty}{i}=\infty.... i really dont see how you got...
[IMG] as you can see, the negative sign is no where 2 be found. Temur where you at when I need you man!
well the residue computation wouldnt be affected by the 1/2 because they derive a Big O bound, so the 1/2 is irrelevant. But this negative sign...
this might be a bit embarrassing but Im having trouble with a simple change of variable in this same integral.. \psi (z) = {1 \over 2\pi...
i dont mean this problem in particular, I suspected I was right the whole time, i mean discussing the theory of RZF in general. I posted this...
whats the name of the courant book, i googled courant and courant zeta and courant riemann and couldnt find anything. The last link is mostly about...
thanks a lot tach and temur, i was afraid i wouldnt get a response. Have any of you studied the theory of RZF rigorously? if so can you offer an...
interesting indeed, although I believe it is irrelevant for my question. Doing some more calculations on wolframalpha, Im 100% sure Im correct, just...
I think you forgot an s in your last equation. \Gamma(\frac{s}{2}+1)=\frac{s}{2}{\Gamma}(\frac{s}{2}) = \frac{1}{2}s\Gamma({s \over 2}). if you...
the original problem is out of William and Fern Ellison's Prime Numbers. I seen Ivic at the library today, maybe I should've grabbed it instead of...
which is also implied by the functional equation of xi, Xi(z) = Xi(1-z) for z=0.
of course it is, why wouldnt it be. Xi is universally defined as \xi (s) = {1 \over 2}s(s-1)\pi^{-s \over 2}\Gamma ({s \over 2}) \zeta (s) and...
not sure what you're asking. The book just states that passing the simple pole leaves a residue of 1/sqrt(z), just as posted above. Basically Im...
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