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## Equidistribution in number theory, an introduction :proceedings of the NATO advanced study institute on equidistribution in number theory#July 11-22, 2005 Granville, Andrew ; Rudnick, Zeév | Springer 2006

Congrès

V

- 345 p.
ISBN 978-1-4020-5403-7

NATO science series II : Mathematics, physics and chemistry , 0237

Localisation : Colloque RdC (MONT)

théorie des nombres # cryptographie # distribution # point de torsion # racine de polynôme # equidistribution # point rationel # problème de Linnik # théorème de Ratner # forme automorphe # application quantique

11-06

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## Angles of Gaussian primes Rudnick, Zeév | CIRM H

Multi angle

y

Research talks

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. 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 ...

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