Distribution of points on Abelian covers over finite fields

Patrick Meisner

doi:10.1142/S1793042118500860

Distribution of points on Abelian covers over finite fields

Patrick Meisner^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We determine in this paper the distribution of the number of points on the covers of ℙ¹(F_q) 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 F_q. In all cases, the distribution is given by a sum of q + 1 random variables.

Original language	English
Pages (from-to)	1375-1401
Number of pages	27
Journal	International Journal of Number Theory
Volume	14
Issue number	5
DOIs	https://doi.org/10.1142/S1793042118500860
State	Published - 1 Jun 2018

Keywords

Curves
finite fields
function fields

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10.1142/S1793042118500860

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AB - 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.

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Distribution of points on Abelian covers over finite fields

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