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- W4300918079 abstract "The Dickson-Guralnick-Zieve curve, briefly DGZ curve, defined over the finite field $mathbb{F}_q$ arises naturally from the classical Dickson invariant of the projective linear group $PGL(3,mathbb{F}_q)$. The DGZ curve is an (absolutely irreducible, singular) plane curve of degree $q^3-q^2$ and genus $frac{1}{2}q(q-1)(q^3-2q-2)+1.$ In this paper we show that the DGZ curve has several remarkable features, those appearing most interesting are: the DGZ curve has a large automorphism group compared to its genus albeit its Hasse-Witt invariant is positive; the Fermat curve of degree $q-1$ is a quotient curve of the DGZ curve; among the plane curves with the same degree and genus of the DGZ curve and defined over $mathbb{F}_{q^3}$, the DGZ curve is optimal with respect the number of its $mathbb{F}_{q^3}$-rational points." @default.
- W4300918079 created "2022-10-04" @default.
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- W4300918079 date "2018-05-15" @default.
- W4300918079 modified "2023-10-16" @default.
- W4300918079 title "On the Dickson-Guralnick-Zieve curve" @default.
- W4300918079 doi "https://doi.org/10.48550/arxiv.1805.05618" @default.
- W4300918079 hasPublicationYear "2018" @default.
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