当前位置: X-MOL 学术J. Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Rational Functions with Small Value Set
Journal of Algebra ( IF 0.9 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.jalgebra.2020.08.039
Daniele Bartoli , Herivelto Borges , Luciane Quoos

Abstract Let q be a prime power, and let F q be the finite field with q elements. In connection with Galois theory and algebraic curves, this paper investigates rational functions h ( x ) = f ( x ) / g ( x ) ∈ F q ( x ) for which the value sets V h = { h ( α ) | α ∈ F q ∪ { ∞ } } are relatively small. In particular, under certain circumstances, it proves that h ( x ) having a small value set is equivalent to the field extension F q ( x ) / F q ( h ( x ) ) being Galois.

中文翻译:

具有小值集的有理函数

摘要 令 q 为素数幂,令 F q 为具有 q 个元素的有限域。结合伽罗瓦理论和代数曲线,本文研究了有理函数 h ( x ) = f ( x ) / g ( x ) ∈ F q ( x ) 其值集 V h = { h ( α ) | α ∈ F q ∪ { ∞ } } 相对较小。特别是,在某些情况下,证明了h(x)具有较小的值集等价于域扩展Fq(x)/Fq(h(x))为Galois。
更新日期:2021-01-01
down
wechat
bug