Angles of Gaussian primes | Vidéo | Carmin.tv

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Angles of Gaussian primes

By Zeév Rudnick

Appears in collections : Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminisme, Exposés de recherche

Fermat showed that every prime $p = 1$ mod $4$ is a sum of two squares: $p = a^2 + b^2$, and hence such a prime gives rise to an angle whose tangent is the ratio $b/a$. Hecke showed, in 1919, that these angles are uniformly distributed, and uniform distribution in somewhat short arcs was given in by Kubilius in 1950 and refined since then. I will discuss the statistics of these angles on fine scales and present a conjecture, motivated by a random matrix model and by function field considerations.

Information about the video

Date of recording 24/05/2017
Date of publication 01/06/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19171503
Cite this video Rudnick, Zeév (24/05/2017). Angles of Gaussian primes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19171503
URL https://dx.doi.org/10.24350/CIRM.V.19171503

Domain(s)

Number Theory

Bibliography

Rudnick, Z., & Waxman, E. (2017). Angles of Gaussian primes. <arXiv:1705.07498> - https://128.84.21.199/abs/1705.07498v1

MSC codes

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