  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 $\mathbb F_p$.
