# HW 8, due Wednesday Nov 9 (updated)

• Let $F=F_2(t)$ be a field with four elements, where $t^2+t+1=0$.  Compute the norm of every element of F.
• Find the values of the parameter $\lambda$ such that $x^2 - y^2 + \lambda z^2=0$ has a singular point in the projective plane.
• Suppose that the zeta function has the form $(1+u+ 3 u^2)/(1-4 u + 3 u^2)$.  (a) What is $q$, the cardinality of the finite field?  (b) Find how many points there are in $F_{q^3}$.
• A zeta function has the form $(1 + a u + 7 u^2)/(1 - 8 u + 7 u^2)$, for some integer a.  (a) What is $q$, the cardinality of the finite field?  (b) If $N_1 = 9$, then what is the integer a?