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arXiv · 1511.00339

Points on singular Frobenius nonclassical curves

Herivelto Borges·Masaaki Homma
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Abstract

In 1990, Hefez and Voloch proved that the number of $F_q$-rational points on a nonsingular plane $q$-Frobenius nonclassical curve of degree $d$ is $N = d(q-d+2)$. We address these curves in the singular setting. In particular, we prove that $d(q-d + 2)$ is a lower bound on the number of $F_q$-rational points on such curves of degree $d$.

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Herivelto Borges, Masaaki Homma. 2015-11-02. Points on singular Frobenius nonclassical curves. https://arxiv.org/abs/1511.00339

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