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Reversed Dickson polynomials of the (k+1)-th kind over finite fields
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fernando, Neranga |
| Copyright Year | 2016 |
| Abstract | Let $p$ be an odd prime. In this paper, we study the permutation behaviour of the reversed Dickson polynomials of the $(k+1)$-th kind $D_{n,k}(1,x)$ when $n=p^{l_1}+3$, $n=p^{l_1}+p^{l_2}+p^{l_3}$, and $n=p^{l_1}+p^{l_2}+p^{l_3}+p^{l_4}$, where $l_1, l_2$, $l_3$, and $l_4$ are non-negative integers. A generalization to $n=p^{l_1}+p^{l_2}+\cdots +p^{l_i}$ is also shown. We find some conditions under which $D_{n,k}(1,x)$ is not a permutation polynomial over finite fields for certain values of $n$ and $k$. We also present a generalization of a recent result regarding $D_{p^l-1,1}(1,x)$ and present some algebraic and arithmetic properties of $D_{n,k}(1,x)$. |
| Starting Page | 234 |
| Ending Page | 255 |
| Page Count | 22 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.jnt.2016.08.018 |
| Alternate Webpage(s) | https://www.math.cmu.edu/~fneranga/Talks/CUNY.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1605.04338v1.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/1706.01391v3.pdf |
| Alternate Webpage(s) | https://www.math.cmu.edu/~fneranga/Talks/UNT.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.jnt.2016.08.018 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
