find the number of analytic functions which vanish only on $S$?
42942
Finding the number of analytic functions which vanish only on a given set.
151171
Distance of nearest zero of an analytic function
141225
Number of all bijective functions from A to A.
86405
Trivial zeros of the Riemann Zeta function
132663
Show $f$ is analytic if $f^8$ is analytic
27865
What is the number of invertible $n\times n$ matrices in $\operatorname{GL}_n(F)$?
103125
Show that a non-constant holomorphic function has zeroes in a compact set
125566
The Identity Theorem for real analytic functions
124971
Find all holomorphic functions with $\Re(f(x+iy))=2xy$
145573
How to show that $f$ is a zero function?
65953
Cardinality of the set of differentiable functions
53848
$f$ holomorphic on $D\setminus \{0\}$ and takes no values in $(-\infty,0],$ then $0$ removable
148512
No analytic function $f$ has modulus $|f(z)|=1/\cosh(\Re z)$
87743
Is a function whose derivative vanishes at rationals constant?
77980
How to check the real analyticity of a function?
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
95494
Number of solutions of an arithmetic function's equation