HOMEWORK 5:

  * This homework assignment is due Friday, June 19.

  POLICY: Homework solutions should be written up in a proper 
  and coherent fashion. It is OK to discuss homework with
  other students or dr.G. Please achknowledge any help received. 
  
  (1) [COMPUTER] [4x5 BONUS pts]  
      Find the prime factorization of the integers
      a[1], a[2], ..., a[p^2]
      in Theorem 4.11
      (where p=3, 5, 7, 13). Include MAPLE (or other)
      CODE and OUTPUT.

  (2) [BONUS 10 pts] [#3, p.92]

  (3) [BONUS 10 pts] [#4, p.92]

  (4) [10 pts] [#5, p.92]
      HINT: Show that G(tau) = F[p](tau)/Delta(tau)
            is modular and has no poles on H and no pole at ioo (infinity).
            Then use Problem (4) in HW 3.


  (5) [10 pts] Let p be prime. Using #4,5 p.92 show that
      tau(pn) = tau(p) tau(n) if (n,p)=1, and
      tau(pn) = tau(p) tau(n) - p^(11) tau(n/p) if (n,p)>1.             

  (6) [10 pts] [#8, p.140]

  (7) [10 pts] [#9, p.140]

  (8) [10 pts] [#10, p.140]