Let $f\in Hol(\mathbb{C}\backslash\{a_1\ldots a_N\})$ where ${a_1\ldots a_N\,\infty}$ are the poles of $f$ show that $f$ is rational function
53191
Showing a meromorphic function is rational
141115
$f$ be an analytic function defined on $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$
132663
Show $f$ is analytic if $f^8$ is analytic
149564
Showing that a function is in $L^1$
48804
Enumeration of rationals from Stein-Shakarchi's Real Analysis (Chapter 1, Exercise 24)
24466
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
17859
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
156727
A step in the proof of Characterization of $W^{1,\infty}$
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
45432
Showing that $f:(0,2\pi]\to S^1$ is not a homeomorphism
157203
Let $\{f_k\}_{k=1}^\infty\in L^{loc}_1(\mathbb R^n)$, show $\{f_k^2\}_{k=1}^\infty$ does not converge in $\mathscr{D}^\prime(\mathbb R^n)$
43177
How do I rigorously show $f(z)$ is analytic if and only if $\overline{f(\bar{z})}$ is?
158502
Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
128658
Analyticity of $\overline {f(\bar z)}$ given $f(z)$ is analytic
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
3801
Functions that take rationals to rationals
12596
Show that $f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in R[x]$ is nilpotent iff $a_0,a_1,a_2,\ldots,a_n$ are nilpotent