Galois points for double-Frobenius nonclassical curves |
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| Institution: | 1. Universidade de São Paulo, Inst. de Ciências Matemáticas e de Computação, São Carlos, SP 13560-970, Brazil;2. Department of Mathematical Sciences, Faculty of Science, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata 990-8560, Japan;1. Dipartimento di Matematica ed Informatica, Università di Perugia, Via Vanvitelli, 60123 Perugia, Italy;2. Dipartimento di Matematica, Informatica ed Economia, Università degli Studi della Basilicata, Viale dell''Ateneo Lucano 10, 85100 Potenza, Italy;1. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, 9000 Gent, Flanders, Belgium;2. Department of Mathematics and Data Science, University of Brussels (VUB), Pleinlaan 2, Building G, 1050 Elsene, Brussels, Belgium;3. Department of Mathematics, University of Rijeka, Radmile Matejčić 2, 51000 Rijeka, Croatia |
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| Abstract: | We determine the distribution of Galois points for plane curves over a finite field of q elements, which are Frobenius nonclassical for different powers of q. This family is an important class of plane curves with many remarkable properties. It contains the Dickson–Guralnick–Zieve curve, which has been recently studied by Giulietti, Korchmáros, and Timpanella from several points of view. A problem posed by the second author in the theory of Galois points is modified. |
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| Keywords: | Galois point Frobenius nonclassical curve Rational point |
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