Moments in the Chebotarev density theorem

In joint work with Régis de la Bretéche and Daniel Fiorilli, we consider weighted
moments for the distribution of Frobenius substitutions in conjugacy classes of
Galois groups of normal number field extensions. The question is inspired by work
of Hooley and recent progress by de la Bretéche–Fiorilli in the case of moments for
primes in arithmetic progressions. As in their work, the results I will discuss are
conditional on the Riemann Hypothesis and confirm that the moments considered
should be Gaussian. Time permitting, I will address a different notion of moments
that can be considered in the same context and that leads to non-Gaussian families
for particular Galois group structures.