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

  • Ferruh ÖzbudakEmail author
  • Zülfükar Saygı
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9061)


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 \({\mathbb F}_q\).


Algebraic curves L-polynomials Rational points 



The first author was partially supported by TÜBİTAK under Grant No. TBAG-112T011.


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© 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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