论文标题
Carlitz的功率总和公式及其应用于有限领域的置换合理功能
A power sum formula by Carlitz and its applications to permutation rational functions of finite fields
论文作者
论文摘要
L. Carlitz在1935年发现的一个公式在有限场的排列有理功能中发现了一个有趣的应用。它允许我们确定第三学位的所有合理功能，这些功能在$ \ bbb f_q $上取消了投影线$ \ bbb p^1（\ bbb f_q）$，这是Ferraguti和Micheli先前通过另一种方法获得的结果。它还允许我们确定在特定条件下$ \ bbb p^1（\ bbb f_q）$的所有4度的所有理性功能。 （完全确定所有有理学功能的4度，该功能是$ \ bbb p^1（\ bbb f_q）$没有任何条件的$ \ bbb p^1（\ bbb f_q）$。）
A formula discovered by L. Carlitz in 1935 finds an interesting application in permutation rational functions of finite fields. It allows us to determine all rational functions of degree three that permute the projective line $\Bbb P^1(\Bbb F_q)$ over $\Bbb F_q$, a result previously obtained by Ferraguti and Micheli through a different method. It also allows us to determine all rational functions of degree four that permute $\Bbb P^1(\Bbb F_q)$ under a certain condition. (A complete determination of all rational functions of degree four that permute $\Bbb P^1(\Bbb F_q)$ without any condition will appear in a separate forthcoming paper.)
