Some remarks on the Picard curves over a finite field

被引：5
|
作者：
Takizawa, Yoh
机构：
[1] Department of Mathematics, Faculty of Science, Chiba University, Inage-ku, Chiba 263-8522
来源：
MATHEMATISCHE NACHRICHTEN | 2007年 / 280卷 / 07期
关键词：
curves; zeta-function; finite fields;
D O I：
10.1002/mana.200410515
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study the Newton polygon of the L-polynomial L(t) associate to the Picard curves y(3) = x(4)-1, y(3) = x(4) - x defined over a finite field F-P. In the former case we get a complete classification. In the latter case we obtained a partial result. As a consequence of our result we obtain a criterion to find a supersingular Picard curves for the above two cases. Our main results are stated in Theorems 3.1 and 4.1. Curves over finite fields. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
引用
收藏
页码：802 / 811
页数：10
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