Sums of two squares over Fq[T]

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-06-01 Epub Date: 2026-02-06 DOI:10.1016/j.ffa.2026.102812

Wentang Kuo, Yu-Ru Liu, Yash Totani

引用次数: 0

Abstract

In this paper, we establish a formula for the number of representations of a polynomial as a norm from a quadratic extension over function fields and study its moments. Our approach involves employing two distinct techniques to derive the main results concerning asymptotic formulas for the moments. The first technique utilizes the framework of Dirichlet series and the second technique involves effectively partitioning the set of polynomials of a fixed degree, providing asymptotic formulas in the limit of large polynomial degree.

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Fq上的两个平方和[T]

本文从函数域上的二次扩展出发，建立了多项式作为范数的表示个数的公式，并研究了它的矩。我们的方法包括采用两种不同的技术来推导有关矩的渐近公式的主要结果。第一种方法是利用Dirichlet级数的框架，第二种方法是对固定次多项式集进行有效的划分，给出大多项式次极限下的渐近公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.