Let be a positive integer, a finite field of cardinality with . In this paper, inspired by [6, 3, 4] and using a slightly different method, we study the fluctuations in the number of -points on the curve given by the affine model , where is drawn at random uniformly from the set of all monic -th power-free polynomials of degree as . The method also enables us to study the fluctuations in the number of -points on the same family of curves arising from the set of monic irreducible polynomials.
Soit un entier, un corps fini de cardinal avec . Dans cet article, inspiré par [6, 3, 4] et en utilisant une méthode légèrement différente, nous étudions les fluctuations du nombre de -points de la courbe donnée par le modèle affine , où parcourt aléatoirement et uniformément l’ensemble des polynômes unitaires, sans puissance -ième, de degré quand . La méthode nous permet aussi d’étudier les fluctuations du nombre de -points de la même famille de courbes provenant de l’ensemble des polynômes unitaires irréductibles.
@article{JTNB_2010__22_3_755_0, author = {Xiong, Maosheng}, title = {The fluctuations in the number of points on a family of curves over a finite field}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {755--769}, publisher = {Universit\'e Bordeaux 1}, volume = {22}, number = {3}, year = {2010}, doi = {10.5802/jtnb.745}, zbl = {1228.11089}, mrnumber = {2769344}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.745/} }
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 SP - 755 EP - 769 VL - 22 IS - 3 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.745/ DO - 10.5802/jtnb.745 LA - en ID - JTNB_2010__22_3_755_0 ER -
%0 Journal Article %A Xiong, Maosheng %T The fluctuations in the number of points on a family of curves over a finite field %J Journal de théorie des nombres de Bordeaux %D 2010 %P 755-769 %V 22 %N 3 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.745/ %R 10.5802/jtnb.745 %G en %F JTNB_2010__22_3_755_0
Xiong, Maosheng. The fluctuations in the number of points on a family of curves over a finite field. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 3, pp. 755-769. doi : 10.5802/jtnb.745. http://archive.numdam.org/articles/10.5802/jtnb.745/
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