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?

 

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s