Zeta-Functions of Curves of Genus 3 over Finite Fields  

作　　者：Fei YU Hong Xi TONG 

机构地区：[1]Science and Technology on Communication Security Laboratory, Chengdu 610041, P. R. China [2]Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第11期2223-2230,共8页数学学报（英文版）

基　　金：Supported by Innovation Fund of Shanghai University (Grant No.A.10-0101-08-407); Shanghai Education Commission,Foundation for Excellent Young High Education Teacher of China (Grant No.B.37-0101-08-006)

摘　　要：In this paper, we determine zeta-functions of some curves of genus 3 over finite fields by gluing three elliptic curves based on Xing＇s research, and the examples show that there exists a maximal curve of genus 3 over F49.In this paper, we determine zeta-functions of some curves of genus 3 over finite fields by gluing three elliptic curves based on Xing＇s research, and the examples show that there exists a maximal curve of genus 3 over F49.

关 键 词：Elliptic curves ZETA-FUNCTIONS Jacobian varieties maximum curves 

分 类 号：O174[理学—数学] TN918.1[理学—基础数学]