# The fluctuations in the number of points on a family of curves over a finite field

Maosheng Xiong^{[1]}

- [1] Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay, Kowloon P. R. China

Journal de Théorie des Nombres de Bordeaux (2010)

- Volume: 22, Issue: 3, page 755-769
- ISSN: 1246-7405

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topXiong, Maosheng. "The fluctuations in the number of points on a family of curves over a finite field." Journal de Théorie des Nombres de Bordeaux 22.3 (2010): 755-769. <http://eudml.org/doc/116433>.

@article{Xiong2010,

abstract = {Let $l \ge 2$ be a positive integer, $\{\mathbb\{F\}\}_q$ a finite field of cardinality $q$ with $q \equiv 1 \hspace\{4.44443pt\}(\@mod \; l)$. In this paper, inspired by [6, 3, 4] and using a slightly different method, we study the fluctuations in the number of $\{\mathbb\{F\}\}_q$-points on the curve $\mathbb\{C\}_F$ given by the affine model $\mathbb\{C\}_F: Y^l=F(X)$, where $F$ is drawn at random uniformly from the set of all monic $l$-th power-free polynomials $F \in \{\mathbb\{F\}\}_q[X]$ of degree $d$ as $d \rightarrow \infty $. The method also enables us to study the fluctuations in the number of $\{\mathbb\{F\}\}_q$-points on the same family of curves arising from the set of monic irreducible polynomials.},

affiliation = {Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay, Kowloon P. R. China},

author = {Xiong, Maosheng},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {curves over finite fields; irreducible polynomials; Dirichlet character},

language = {eng},

number = {3},

pages = {755-769},

publisher = {Université Bordeaux 1},

title = {The fluctuations in the number of points on a family of curves over a finite field},

url = {http://eudml.org/doc/116433},

volume = {22},

year = {2010},

}

TY - JOUR

AU - Xiong, Maosheng

TI - The fluctuations in the number of points on a family of curves over a finite field

JO - Journal de Théorie des Nombres de Bordeaux

PY - 2010

PB - Université Bordeaux 1

VL - 22

IS - 3

SP - 755

EP - 769

AB - Let $l \ge 2$ be a positive integer, ${\mathbb{F}}_q$ a finite field of cardinality $q$ with $q \equiv 1 \hspace{4.44443pt}(\@mod \; l)$. In this paper, inspired by [6, 3, 4] and using a slightly different method, we study the fluctuations in the number of ${\mathbb{F}}_q$-points on the curve $\mathbb{C}_F$ given by the affine model $\mathbb{C}_F: Y^l=F(X)$, where $F$ is drawn at random uniformly from the set of all monic $l$-th power-free polynomials $F \in {\mathbb{F}}_q[X]$ of degree $d$ as $d \rightarrow \infty $. The method also enables us to study the fluctuations in the number of ${\mathbb{F}}_q$-points on the same family of curves arising from the set of monic irreducible polynomials.

LA - eng

KW - curves over finite fields; irreducible polynomials; Dirichlet character

UR - http://eudml.org/doc/116433

ER -

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