FoCM 2014 conference

Workshop A3 - Computational Number Theory

December 11, 15:50 ~ 16:30 - Room A21

## Distribution of traces of genus 3 curves

### University Rennes 1, France   -   ritzenthalerchristophe@gmail.com

We present numerical experiments to visualize the asymmetry in the distribution of traces of Frobenius of genus $3$ curves over finite fields. These observations are linked to the so-called Serre obstruction for non hyperelliptic curves. We also give a heuristic explaination for the phenomena we observe.

Joint work with Reynald Lercier (university Rennes 1), Florent Rovetta (university Aix-Marseille), Jeroen Sijsling (Dartmouth college) and Ben Smith (Polytechnique Paris).