Homework #11 Due 8:10am December 3, 2008
Section 87 #1, #5
Section 87 #6 (for this problem, you will need Rouche’s theorem, which we
will prove in class on Monday, Dec. 1)
Additional problem #1:
Let Edenote the result of glueing Cto itself via the maps f1(z) = z+ 1
and f2(z) = z+i(as demonstrated in class).
It is a fact that an analytic function f:E→Cis equivalent to an
analytic function ˜g:C→Csatisfying ˜g(z+ 1) = ˜g(z) and ˜g(z+i) = ˜g(z).
Compute the dimension of {f:E→C|f is analytic }as a complex
vector space.
1