Reciprocal polynomials and curves with many points over a finite field

被引：3

作者：

Gupta, Rohit ^{[1
]}

Mendoza, Erik A. R. ^{[2
]}

Quoos, Luciane ^{[2
]}

机构：

[1] Birla Inst Technol & Sci Pilani, Dept Math, Hyderabad Campus, Hyderabad 500078, Telangana, India

[2] Univ Fed Rio de Janeiro, Inst Matemat, Cidade Univ, BR-21941909 Rio de Janeiro, Brazil

来源：

RESEARCH IN NUMBER THEORY | 2023年 / 9卷 / 03期

关键词：

Function fields; Algebraic curves; Kummer extensions; Rational points; RATIONAL-POINTS; KUMMER COVERS; FIBER PRODUCTS; NUMBER; GENUS;

D O I：

10.1007/s40993-023-00464-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F(q)2 be the finite field with q(2) elements. We provide a simple and effective method, using reciprocal polynomials, for the construction of algebraic curves over F(q)2 with many rational points. The curves constructed are Kummer covers or fiber products of Kummer covers of the projective line. Further, we compute the exact number of rational points for some of the curves.

引用

页数：23

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