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

  title={Riemann zeros in radiation patterns: II. Fourier transforms of zeta},
  author={Michael V. Berry},
  journal={Journal of Physics A},
  • 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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