Frobenius matrices and a variant of Zolotarev's theorem

Hai-Liang Wu; Li-Yuan Wang

Frobenius matrices and a variant of Zolotarev's theorem

Number Theory 2021-01-28 v2

Authors: Hai-Liang Wu , Li-Yuan Wang

Abstract

In this paper, with the help of the theory of matrices and finite fields we generalize Zolotarev's theorem to an arbitrary finite dimensional vector space over $\mathbb{F}_q$ , where $\mathbb{F}_q$ denotes the finite field with $q$ elements.

Keywords

frobenius matrices zolotarev's theorem finite fields vector spaces

Cite

@article{arxiv.2101.05558,
  title  = {Frobenius matrices and a variant of Zolotarev's theorem},
  author = {Hai-Liang Wu and Li-Yuan Wang},
  journal= {arXiv preprint arXiv:2101.05558},
  year   = {2021}
}

Comments

Our result is not new, which was obtained by Prof. P.L. Clark and Prof. A. Brunyate in the paper Extending the Zolotarev-Frobenius approach to quadratic reciprocity (pubished in the Ramanujan journal)

Frobenius matrices and a variant of Zolotarev's theorem

Abstract

Keywords

Cite

Comments

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