The Stoehr-Voloch approach has been largely used to deal with the classical problem of estimating the number of rational points of a Fermat curve over a finite field. The same method actually applies to any curve admitting as an automorphism group the direct product of two cyclic groups C_1 and C_2 of the same size k, and such that the quotient curves with respect to both C_1 and C_2 are rational. In this paper such a curve is called a generalized Fermat curve. Our main achievement is that of extending some known results on Fermat curves to generalized Fermat curves.
ON THE NUMBER OF RATIONAL POINTS OF GENERALIZED FERMAT CURVES OVER FINITE FIELDS
GIULIETTI, Massimo
2012
Abstract
The Stoehr-Voloch approach has been largely used to deal with the classical problem of estimating the number of rational points of a Fermat curve over a finite field. The same method actually applies to any curve admitting as an automorphism group the direct product of two cyclic groups C_1 and C_2 of the same size k, and such that the quotient curves with respect to both C_1 and C_2 are rational. In this paper such a curve is called a generalized Fermat curve. Our main achievement is that of extending some known results on Fermat curves to generalized Fermat curves.File in questo prodotto:
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