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

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Part of the book series:Lecture Notes in Computer Science ((LNTCS,volume 9061))

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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\({\mathbb F}_q\).

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Acknowledgment

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

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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, Dumlupınar Bul., No:1, 06800, Ankara, Turkey

    Ferruh Özbudak

  2. Institute of Applied Mathematics, Middle East Technical University, Dumlupınar Bul., No:1, 06800, Ankara, Turkey

    Ferruh Özbudak

  3. Department of Mathematics, TOBB University of Economics and Technology, Söğütözü, 06530, Ankara, Turkey

    Zülfükar Saygı

Authors
  1. Ferruh Özbudak

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  2. Zülfükar Saygı

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Correspondence toFerruh Özbudak.

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Editors and Affiliations

  1. Department of Computer Science, Univ of California, Santa Barbara, Santa Barbara, California, USA

    Çetin Kaya Koç

  2. University of Paris VIII, Paris, France

    Sihem Mesnager

  3. Sabancı University, Istanbul, Turkey

    Erkay Savaş

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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. https://doi.org/10.1007/978-3-319-16277-5_10

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