4
votes
2answers
231 views

Some identities with the Riemann zeta function

Can someone either help derive or give a reference to the identities in Appendix B, page 27 of this, http://arxiv.org/pdf/1111.6290v2.pdf Here is a reproduction of Appendix B from Klebanov, Pufu, ...
7
votes
0answers
850 views

Is this Fourier like transform equal to the Riemann zeta function?

This question builds upon the answer to this question. This new question has only minor changes compared to the previous question, but the scale factor of the output from the Fourier like transform is ...
2
votes
0answers
190 views

Are the amplitudes of these frequency spikes equal to 1 when the real part of the complex number “s” is equal to one half?

Over at stack overflow I asked a question about how to plot the Riemann zeta zero spectrum from the von Mangoldt function. Then I asked a question about calculating the Riemann zeta function at the ...
28
votes
1answer
1k views

Are these zeros equal to the imaginary parts of the Riemann zeta zeros?

Edit 8.8.2013: See this question also. The Fourier cosine transform of an exponential sawtooth wave times $e^{-x/2}$: $$\operatorname{FourierCosineTransform}(\operatorname{SawtoothWave}(e^x)\cdot ...
2
votes
0answers
207 views

What are the local minima in this spectrum?

Edit 6.2.2012: The sequence to be transformed should be f = 0,1,2,3,4,5... which makes the mentioning of the von Mangoldt function less necessary. Edit 5.2.2012: I had the wrong plot of the insignal. ...
2
votes
0answers
208 views

Why Pólya's method is wrong?

By truncating the Fourier transform, Pólya managed to prove that the Xi function on the critical line was approximately $$\xi(1/2+is) = (2\pi)^2 ( K_{9/4+is/2}( 2\pi) +K_{9/4-is/2}( 2\pi))$$ If this ...