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arXiv · 2406.13687

Diffraction of the primes and other sets of zero density

Adam Humeniuk·Christopher Ramsey·Nicolae Strungaru
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Abstract

In this paper, we show that the diffraction of the primes is absolutely continuous, showing no bright spots (Bragg peaks). We introduce the notion of counting diffraction, extending the classical notion of (density) diffraction to sets of density zero. We develop the counting diffraction theory and give many examples of sets of zero density of all possible spectral types.

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Adam Humeniuk, Christopher Ramsey, Nicolae Strungaru. 2024-06-19. Diffraction of the primes and other sets of zero density. https://doi.org/10.1017/s1446788725000096

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