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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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Department of Mathematics, Middle East Technical University, Dumlupınar Bul., No:1, 06800, Ankara, Turkey
Ferruh Özbudak
Institute of Applied Mathematics, Middle East Technical University, Dumlupınar Bul., No:1, 06800, Ankara, Turkey
Ferruh Özbudak
Department of Mathematics, TOBB University of Economics and Technology, Söğütözü, 06530, Ankara, Turkey
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Correspondence toFerruh Özbudak.
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Department of Computer Science, Univ of California, Santa Barbara, Santa Barbara, California, USA
Çetin Kaya Koç
University of Paris VIII, Paris, France
Sihem Mesnager
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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