Newbetuts

If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.

If $f$ is an entire function and $f(z) \not \in [0,1]$ for every $z$, then $f$ is constant

How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?

Measure of set where holomorphic function is large

Is there an entire function with $f(\mathbb{Q}) \subset \mathbb{Q}$ and a non-finite power series representation having only rational Coeffitients

If $f: \mathbb{C} \to \mathbb{C}$ is continuous and analytic off $[-1,1]$ then is entire.

Entire functions that satisfy $f(x) = |x^k|$ for all $x$ real in $(-1, 1)$, for some odd integer $k$

Entire function $f(z)$ grows like $\exp(x^\pi)$ as $x\to+\infty$

Is every entire function is a sum of an entire function bounded on every horizontal strip and an entire function bounded on every vertical strip?

Fermat's last theorem for entire functions

$f$ is entire, prove that $\{f_n = f(nz) | n \in \mathbb{N}\}$ is normal on the annulus iff $f$ is constant

Prove that a square-integrable entire function is identically zero

Entire function with arbitrary zeroes $(a_n)$ but $|a_n| \to a \neq \infty$

$f(ax)=f(x)^2-1$, what is $f$?

Proving that a doubly-periodic entire function $f$ is constant.

New posts in entire-functions

Does the set of entire functions have the same cardinality as the reals?

If $f$ is an entire function of order $\lambda$ then $f'$ also has order $\lambda$

Entire function satisfying an iteration formula

If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.

If $f$ is an entire function and $f(z) \not \in [0,1]$ for every $z$, then $f$ is constant

How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?

Measure of set where holomorphic function is large

Is there an entire function with $f(\mathbb{Q}) \subset \mathbb{Q}$ and a non-finite power series representation having only rational Coeffitients

If $f: \mathbb{C} \to \mathbb{C}$ is continuous and analytic off $[-1,1]$ then is entire.

Entire functions that satisfy $f(x) = |x^k|$ for all $x$ real in $(-1, 1)$, for some odd integer $k$

Entire function $f(z)$ grows like $\exp(x^\pi)$ as $x\to+\infty$

Is every entire function is a sum of an entire function bounded on every horizontal strip and an entire function bounded on every vertical strip?

Fermat's last theorem for entire functions

$f$ is entire, prove that $\{f_n = f(nz) | n \in \mathbb{N}\}$ is normal on the annulus iff $f$ is constant

Prove that a square-integrable entire function is identically zero

Entire function with arbitrary zeroes $(a_n)$ but $|a_n| \to a \neq \infty$

$f(ax)=f(x)^2-1$, what is $f$?

Proving that a doubly-periodic entire function $f$ is constant.