Abstract
In 1990, Hefez and Voloch proved that the number of \(\mathbb {F}_q\)-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 \(\mathbb {F}_q\)-rational points on such curves of degree d.
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Acknowledgments
The first author was supported by FAPESP Grant Number 2015/03984-7.
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Borges, H., Homma, M. Points on singular Frobenius nonclassical curves. Bull Braz Math Soc, New Series 48, 93–101 (2017). https://doi.org/10.1007/s00574-016-0008-6
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DOI: https://doi.org/10.1007/s00574-016-0008-6