Riemann zeros in radiation patterns: II. Fourier transforms of zeta

@article{Berry2015RiemannZI,
  title={Riemann zeros in radiation patterns: II. Fourier transforms of zeta},
  author={Michael V. Berry},
  journal={Journal of Physics A},
  year={2015},
  volume={48},
  pages={385203}
}
  • M. Berry
  • Published 1 September 2015
  • Mathematics
  • Journal of Physics A
This extends a previous study (2012 J. Phys. A: Math. Theor. 45 302001) of two initial waveforms whose far-field radiation patterns possess sidelobes separated by the Riemann zeros. The analysis suffered from the disadvantage that the sidelobes were very weak, making it difficult to detect the zeros between them. To overcome this, new Fourier pairs are derived, whose sidelobes are not weak. These are transforms of the zeta function on the critical line, modulated by functions with no zeros on… 
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References

SHOWING 1-6 OF 6 REFERENCES
Riemann zeros in radiation patterns
Propagation into the far field changes initial waves into their Fourier transforms. This implies that the Riemann zeros could be observed experimentally in the radiation pattern generated by an…
Computer-generated holography as a generic display technology
Computer-generated holography technique is a powerful technology suitable for a wide range of display types, including 2D, stereoscopic, autostereoscopic, volumetric, and true 3D imaging.…
Digital spatial light modulators
Spatial control of the phase and amplitude of a laser beam is useful for applications ranging from imaging and holography to interferometry and optical tweezers, reports Neil Savage.
Riemann's Zeta Function
An electro-mechanical investigation of the Riemann zeta function in the critical strip
Riemann’s Zeta Function (Mineola
  • 2001