2021/05/06 by Devin, Lucile
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2105.02492
Motivated by questions of Fouvry and Rudnick on the distribution of Gaussian primes, we develop a very general setting in which one can study inequities in the distribution of analogues of primes through analytic properties of infinitely many L-functions. In particular, we give a heuristic argument for the following claim : for more than half of the prime numbers that can be written as a sum of two square, the odd square is the square of a positive integer congruent to 1 \bmod 4.