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Angles of Gaussian primes
Multi angle
Authors : ... (Author of the conference)
... (Publisher )
11F66 - Langlands L-functions; one variable Dirichlet series and functional equations
11M06 - $ \zeta (s)$ and $L(s, \chi)$
11M26 - Nonreal zeros of $ \zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
11R44 - Distribution of prime ideals
11T55 - Arithmetic theory of polynomial rings over finite fields
11M50 - Relations with random matrices
... (Publisher )
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Abstract :
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.
MSC Codes : 11F66 - Langlands L-functions; one variable Dirichlet series and functional equations
11M06 - $ \zeta (s)$ and $L(s, \chi)$
11M26 - Nonreal zeros of $ \zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
11R44 - Distribution of prime ideals
11T55 - Arithmetic theory of polynomial rings over finite fields
11M50 - Relations with random matrices
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Information on the Video
Language : EnglishAvailable date : 01/06/17 Conference Date : 24/05/17 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:42:13 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-05-24_Rudnick.mp4 
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Information on the Event
Event Title : Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminismeDates : 22/05/17 - 26/05/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1595.html
Citation Data
DOI : 10.24350/CIRM.V.19171503Cite this video as: (2017). Angles of Gaussian primes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19171503 URI : http://dx.doi.org/10.24350/CIRM.V.19171503 |
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Bibliography
- Rudnick, Z., & Waxman, E. (2017). Angles of Gaussian primes.
