Statistics for biquadratic covers of the projective line over finite fields

Research output: Contribution to journalArticleScientificpeer-review

Researchers

  • Elisa Lorenzo
  • Giulio Meleleo
  • Piermarco Milione
  • Alina Bucur

Research units

  • Universiteit Leiden
  • Roma Tre University
  • University of Barcelona
  • University of California

Abstract

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.

Details

Original languageEnglish
Pages (from-to)448-477
JournalJournal of Number Theory
Volume173
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

    Research areas

  • Function fields, Biquadratic curves, Biquadratic covers, Number of points over finite fields, Arithmetic statistics

ID: 11678241