- Universiteit Leiden
- Roma Tre University
- University of Barcelona
- University of California
We study the distribution of the traces of the Frobenius endomorphisms of genus g curves which are quartic non-cyclic covers of View the MathML sourcePFq1, as the curve varies in an irreducible component of the moduli space. We show that for q fixed, the limiting distribution of the traces of Frobenius equals the sum of q+1q+1 independent random discrete variables. We also show that when both g and q go to infinity, the normalized trace has a standard complex Gaussian distribution. Finally, we extend these computations to the general case of arbitrary covers of View the MathML sourcePFq1 with Galois group isomorphic to r copies of Z/2ZZ/2Z. For r=1r=1 we recover the already known results for the family of hyperelliptic curves.
|Julkaisu||Journal of Number Theory|
|Tila||Julkaistu - 2017|
|OKM-julkaisutyyppi||A1 Julkaistu artikkeli, soviteltu|