论文标题
关于有限领域的算术进行的
On arithmetic progressions in finite fields
论文作者
论文摘要
在本文中，我们探讨了$ \ mathbb {f} _ {q^n} $中的$ m $ termtrs算术进度的存在，其术语都是原始的元素，并且其中至少一个是正常的。我们获得了$ M \ ge 4 $的渐近结果，并获得$ m \ in \ {2,3 \} $的具体结果，当共同差异属于$ \ MATHBB {f} _ {q} _ {q}^*$时，例外的完整列表。这些证明结合了使用软件SageMath的字符总和，筛子估计和计算参数。
In this paper, we explore the existence of $m$-terms arithmetic progressions in $\mathbb{F}_{q^n}$ with a given common difference whose terms are all primitive elements, and at least one of them is normal. We obtain asymptotic results for $m \ge 4$ and concrete results for $m \in \{2,3\}$, where the complete list of exceptions when the common difference belongs to $\mathbb{F}_{q}^*$ is obtained. The proofs combine character sums, sieve estimates, and computational arguments using the software SageMath.
