تقرير
Primitive normal Values of rational functions with one prescribed norm and trace over finite fields
| العنوان: | Primitive normal Values of rational functions with one prescribed norm and trace over finite fields |
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| المؤلفون: | Mazumder, Arpan Chandra, Basnet, Dhiren Kumar |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 12E20, 11T23 |
| الوصف: | Let $q, n, m \in \mathbb{N}$ be such that $q$ is a prime power and $a, b \in \mathbb{F}$. In this article we establish a sufficient condition for the existence of a primitive normal pair $(\alpha, f(\alpha)) \in \mathbb{F}_{q^m}$ over $\mathbb{F}$ with a prescribed primitive norm $a$ and a non-zero trace $b$ over $\mathbb{F}$ of $\alpha$, where $f(x) \in \mathbb{F}_{q^m}(x)$ is a rational function of degree sum $n$ with some minor restrictions. Furthermore, for $q=7^k$, $m \geq 7$ and rational functions with numerator and denominator being linear, we explicitly find at most 6 fields in which the desired pair may not exist. Comment: 16 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.05298 |
| رقم الأكسشن: | edsarx.2405.05298 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |