On algebraic degrees of inverted Kloosterman sums

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-08-01 DOI:10.1016/j.ffa.2024.102477

Xin Lin , Daqing Wan

引用次数: 0

Abstract

The study of n-dimensional inverted Kloosterman sums was suggested by Katz (1995) [7] who handled the case when $n = 1$ from complex point of view. For general $n \geq 1$ , the n-dimensional inverted Kloosterman sums were studied from both complex and p-adic point of view in our previous paper (2024) [10]. In this note, we study the algebraic degree of the inverted n-dimensional Kloosterman sum as an algebraic integer.

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论倒克罗斯特曼和的代数度

n 维倒克罗斯特曼和的研究是由 Katz（1995）[7] 提出的，他从复数角度处理了 n=1 的情况。对于一般 n≥1，我们在之前的论文 (2024) [10] 中从复数和 p-adic 角度研究了 n 维倒克洛斯特曼和。在本注释中，我们将研究作为代数整数的 n 维克罗斯特曼倒数和的代数度。

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.