Master's Thesis presentation, Victor Ahlquist

We study the low-lying zeros of Artin L-functions associated to non-Galois cubic number fields through their one- and two-level densities. By studying previous work, we find a symmetry in the one-level density, which has not previously been pointed out. Furthermore, we obtain new precise estimates for the two-level density, both through unconditional calculations and by applying the L-function Ratios Conjecture. In particular, we detect a new type of phase transition in the lower-order terms of the two-level density.

Handledare: Anders Södergren
Examinator: Julia Brandes