Zero set of a non constant analytic function.

Question

Is there any example of a non constant analytic function on { z : |z|<1} , which have infinite zeros in that domain?

You might contrast your problem and its solution to the discussion at https://math.stackexchange.com/questions/1232039/can-a-non-constant-analytic-function-have-infinitely-many-zeros-on-a-closed-disk , where your open disk is replaced with a closed disk. — Eric Towers, Apr 03 '20 at 06:47

score 1 · Accepted Answer · answered Apr 03 '20 at 06:34

1

$f(z)=\sin (\frac {\pi} {1-z})$ has zeros at $1-\frac 1 n, n=1,2,3,...$.

answered Apr 03 '20 at 06:34

Kavi Rama Murthy

1 Answers1