Abstract
AbstractLet 𝓧 be the nonsingular model of a plane curve of typeyn=f(x) over the finite fieldFof orderq2, wheref(x) is a separable polynomial of degree coprime ton. If the number ofF-rational points of 𝓧 attains the Hasse–Weil bound, then the condition thatndividesq+1 is equivalent to the solubility off(x) inF; see [20]. In this paper, we investigate this condition forf(x) =xℓ(xm+1).
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