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

Conference paper

DOI: 10.1007/978-3-319-16277-5_10

Volume 9061 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Özbudak F., Saygı Z. (2015) L-Polynomials of the Curve \(\displaystyle y^{q^n}-y=\gamma x^{q^h+1} - \alpha \) over \({\mathbb F}_{q^m}\). In: Koç Ç., Mesnager S., Savaş E. (eds) Arithmetic of Finite Fields. WAIFI 2014. Lecture Notes in Computer Science, vol 9061. Springer, Cham

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 

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