2016/12/11 by Patrick Meisner
Computer Science · Mathematics · #Abelian extension #Abelian group #Analytic Number Theory Research #Coding theory and cryptography #Distribution (mathematics) #Extension (predicate logic) #Field (mathematics) #Finite field #Fixed point #Limits and Structures in Graph Theory #math.NT
paper · pdf · doi:10.1142/s1793042118500860
arxiv created 2016/12/11 · openalex publication_date 2017/12/04 · arxiv updated 2017/12/15 · openalex created_date 2017/12/22 · openalex updated_date 2026/08/05
We determine in this paper the distribution of the number of points on the covers of [Formula: see text] such that [Formula: see text] is a Galois extension and [Formula: see text] is abelian when [Formula: see text] is fixed and the genus, [Formula: see text], tends to infinity. This generalizes the work of Kurlberg and Rudnick and Bucur, David, Feigon and Lalin who considered different families of curves over [Formula: see text]. In all cases, the distribution is given by a sum of [Formula: see text] random variables.