L-Polynomials of the Curve \(\displaystyle y^{q^n}-y=\gamma x^{q^h+1} - \alpha \) over \({\mathbb F}_{q^m}\)

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)

Abstract

Let \(\chi \) be a smooth, geometrically irreducible and projective curve over a finite field \({\mathbb F}_q\) of odd characteristic. The L-polynomial \(L_\chi (t)\) of \(\chi \) determines the number of rational points of \(\chi \) not only over \({\mathbb F}_q\) but also over \({\mathbb F}_{q^s}\) for any integer \(s \ge 1\). In this paper we determine L-polynomials of a class of such curves over \({\mathbb F}_q\).

Keywords

Algebraic curves L-polynomials Rational points 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  3. 3.Department of MathematicsTOBB University of Economics and TechnologyAnkaraTurkey

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