Mathematics > Algebraic Geometry
[Submitted on 12 Jul 2018]
Title:Number of Rational points of the Generalized Hermitian Curves over $\mathbb F_{p^n}$
View PDFAbstract:In this paper we consider the curves $H_{k,t}^{(p)} : y^{p^k}+y=x^{p^{kt}+1}$ over $\mathbb F_p$ and and find an exact formula for the number of $\mathbb F_{p^n}$-rational points on $H_{k,t}^{(p)}$ for all integers $n\ge 1$. We also give the condition when the $L$-polynomial of a Hermitian curve divides the $L$-polynomial of another over $\mathbb F_p$.
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