Distribution of points on Abelian covers over finite fields

Patrick Meisner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We determine in this paper the distribution of the number of points on the covers of ℙ1(Fq) such that K(C) is a Galois extension and Gal(K(C)/K) is abelian when q is fixed and the genus, g, tends to infinity. This generalizes the work of Kurlberg and Rudnick and Bucur, David, Feigon and Lalin who considered different families of curves over Fq. In all cases, the distribution is given by a sum of q + 1 random variables.

Original languageEnglish
Pages (from-to)1375-1401
Number of pages27
JournalInternational Journal of Number Theory
Issue number5
StatePublished - 1 Jun 2018


  • Curves
  • finite fields
  • function fields


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