JOURNAL ARTICLE
关于Bernoulli-Goss多项式的一些注记
Year: 1989 Journal: Science in China Series A-Mathematics Physics Astronomy & Technological Science (in Chinese) Vol: 19 (12)Pages: 1257-1263 Publisher: Science China Press
Abstract
Goss和冯克勤证明了:对q≥2,Fq[T]中存在无穷多不正规的不可约多项式. Ireland和Small给出了第n个Bernoulli-Goss多项式(1≤n≤p2—1)的明确表达式,利用这个结果,他们对于3≤p≤269求出所有形为T2—a(a∈FP[T])的正规二次不可约多项式. 本文对n有两项q-adic展开的情形,给出Fq[T]中第n个Bernoulli-Goss多项式的明确表达式. 由此证明了:对任意q≥3,Fq[T]中存在无穷多不可约多项式同时是第一类和第二类不正规的,我们还给出二次不可约多项式正规性的一些等价条件. 基于文献[3]中的计算结果,我们决定出特征不超过269的所有Fq[T]中二次正规不可约多项式.
Keywords:
Combinatorics Physics Mathematics
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advanced mathematical theories
Physical Sciences → Mathematics → Mathematical Physics
Advanced Algebra and Geometry
Physical Sciences → Mathematics → Mathematical Physics
Algebraic Geometry and Number Theory
Physical Sciences → Mathematics → Geometry and Topology
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