Angles of Gaussian primes

Sun, 29/04/2018 - 12:00

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 $b/a$. Do these angles exhibit order or randomness? I will discuss the statistics of these angles and present a conjecture, motivated by a random matrix model and by function field considerations.