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# Collection Prime numbers and automatic sequences: determinism and randomness / Nombres premiers et suites automatiques : aléa et déterminisme

Organizer(s) Dartyge, Cécile ; Drmota, Michael ; Martin, Bruno ; Mauduit, Christian ; Rivat, Joël ; Stoll, Thomas
Date(s) 5/22/17 - 5/26/17
00:00:00 / 00:00:00
1 5

## Angles of Gaussian primes

Also appears in collection : 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.

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• 42:13
published on June 1, 2017

## Angles of Gaussian primes

By Zeév Rudnick

32:38
published on June 1, 2017

## Bounded remainder sets for the discrete and continuous irrational rotation

49:35
published on June 1, 2017

## Large gaps between primes in subsets

By James Maynard

44:58
published on June 1, 2017

## Large character sums

By Youness Lamzouri

41:55
published on June 1, 2017

## Small sumsets in continuous and discrete settings

By Anne de Roton

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