HOMEWORK 2:

  * This homework assignment is due Friday, May 29.

  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) [BONUS 20 pts] [#4 p.23]
      Assume w2/w1 is not real.
      Suppose f has periods w1, w2 and f is even.
      Let Omega=Omega(w1,w2).
      Prove that f is a rational function of the
      Weiestrass p-function p(z)=p(z,Omega).

      HINTS:
      (i) Suppose the poles of f are contained in Omega.
          Prove that f can be written as a polynomial in p(z):
          f(z) = a[0] + a[1]p(z) + ... a[n] (p(z))^n
          where the a[i] in C.
      (ii) In general show that for some polynomial P(x)
           g(z) = f(z) P( p(z) )
           and the poles of g(z) are contained in Omega.
           NOTE: Here p(z) is the Weierstrass p-function
                 p(z)=p(z,Omega).

  (2) [10 pts] [# 5 p.23]
      [HINT:  f(z) = (f(z)+f(-z))/2  + (f(z)-f(-z))/2]

  (3) [BONUS 10 pts] [#6 p.23]

  (4) [10 pts] [#9 p.24]
      [HINT: Theorem 1.14 is useful]

  (5) [BONUS 10 pts] [#10 p.24]
      [HINT: Consider f'(z)/f(z)]

  (6) [10 pts] [#11 p.24]


  (7) [10 pts] [#12 p.24]


  (8) [10 pts] [#13 p.24]