Angles of Gaussian primes
DATE:2017-04-13
Speaker
:Zeév Rudnick (Tel Aviv University)
Venue
: B924
Time
: 2017年04月14日 16:00-17:30
Title
: Title: Angles of Gaussian Primes.
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.
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