有限域子群元素间的双重和三重特征和与间隙

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-04-10 DOI:10.1142/s1793042124500842

Jiankang Wang, Zhefeng Xu

引用次数: 0

摘要

对于奇素数 p，让 𝔽p 成为 p 元素的有限域。本文的主要目的是建立关于有限域乘法子群元素间差距的新结果。对于任意 a,b,c∈𝔽p∗，我们还得到了以下双特征和 Ta,b,c(χ,ℋ1、ℋ2)=∑h1∈ℋ1∑h2∈ℋ2χ(a+bh1+ch2)和三重特征和 Sχ(a,b,ℋ1,ℋ2,𝒩)=∑x∈𝒩∑h1∈ℋ1∑h2∈ℋ2χ(x+ah1+bh2)，其中𝒩={1,...,N}，且乘法子群ℋ1,ℋ2⊆𝔽p∗分别为阶 H1 和 H2。

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Double and triple character sums and gaps between the elements of subgroups of finite fields

For an odd prime $p$ , let $𝔽_{p}$ be the finite field of $p$ elements. The main purpose of this paper is to establish new results on gaps between the elements of multiplicative subgroups of finite fields. For any $a, b, c \in 𝔽_{p}^{*}$ , we also obtain new upper bounds of the following double character sum $T_{a, b, c} (χ, ℋ_{1}, ℋ_{2}) = \sum_{h_{1} \in ℋ_{1}} \sum_{h_{2} \in ℋ_{2}} χ (a + b h_{1} + c h_{2})$ and a triple character sum $S_{χ} (a, b, ℋ_{1}, ℋ_{2}, 𝒩) = \sum_{x \in 𝒩} \sum_{h_{1} \in ℋ_{1}} \sum_{h_{2} \in ℋ_{2}} χ (x + a h_{1} + b h_{2})$ with $𝒩 = {1, \dots, N}$ and multiplicative subgroups $ℋ_{1}, ℋ_{2} \subseteq 𝔽_{p}^{*}$ of order $H_{1}$ and $H_{2}$ , respectively.

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.