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Points on singular Frobenius nonclassical curves

  • Herivelto BorgesEmail author
  • Masaaki Homma
Article

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.

Keywords

Algebraic curve Frobenius nonclassical curve Finite Field 

Mathematics Subject Classification

Primary 14H45 Secondary 14Hxx 

Notes

Acknowledgments

The first author was supported by FAPESP Grant Number 2015/03984-7.

References

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Copyright information

© Sociedade Brasileira de Matemática 2016

Authors and Affiliations

  1. 1.ICMCUniversidade de São PauloSão CarlosBrazil
  2. 2.Department of Mathematics and PhysicsKanagawa UniversityHiratsukaJapan

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