Fq-primitive points on varieties over finite fields

IF 1.2 3区数学 Q1 MATHEMATICS Finite Fields and Their Applications Pub Date : 2025-01-24 DOI:10.1016/j.ffa.2025.102582

Soniya Takshak , Giorgos Kapetanakis , Rajendra Kumar Sharma

引用次数: 0

Abstract

Let r be a positive divisor of

q - 1

and

f (x, y)

a rational function of degree sum d over

F_{q}

with some restrictions, where the degree sum of a rational function

f (x, y) = f_{1} (x, y) / f_{2} (x, y)

is the sum of the degrees of

f_{1} (x, y)

and

f_{2} (x, y)

. In this article, we discuss the existence of triples

(α, β, f (α, β))

over

F_{q}

, where

α, β

are primitive and

f (α, β)

is an r-primitive element of

F_{q}

. In particular, this implies the existence of

F_{q}

-primitive points on the surfaces of the form

z^{r} = f (x, y)

. As an example, we apply our results on the unit sphere over

F_{q}

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.

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