query: entire function with bounded multiplicity is a polynomial
positive_passages.docid: 152347
positive_passages.text: Proof that a certain entire function is a polynomial
negative_passages.docid: 79359
negative_passages.text: Show that $f$ is a polynomial if it's the uniform limit of polynomais
negative_passages.docid: 118085
negative_passages.text: complex polynomial satisfying inequality
negative_passages.docid: 1954
negative_passages.text: Entire function bounded by polynomial of degree 3/2 must be linear.
negative_passages.docid: 105172
negative_passages.text: Prove that the entire function is constant over certain conditions.
negative_passages.docid: 69804
negative_passages.text: Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
negative_passages.docid: 7878
negative_passages.text: Proving that a doubly-periodic entire function $f$ is constant.
negative_passages.docid: 62268
negative_passages.text: Doubly periodic entire function with periods that are linearly independent over $\mathbb{Q}$ is constant.
negative_passages.docid: 135129
negative_passages.text: Proving an entire  function which misses a ball is constant
negative_passages.docid: 20907
negative_passages.text: Entire function, Liouville and zeroes
negative_passages.docid: 82371
negative_passages.text: $f$ is an entire function with Im $f\geq 0$
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 107518
negative_passages.text: Entire function $f$ such that $|f(z)| ≤ K |z|^3$ for $|z|\ge1$ and $f(z) = f(iz)$ for every $z∈C$
negative_passages.docid: 6722
negative_passages.text: to show $f$ is a polynomial in $z$
negative_passages.docid: 80397
negative_passages.text: Show that this set of polynomials is ideal in F[x]
negative_passages.docid: 62251
negative_passages.text: "Maximum common divisor" for entire functions
negative_passages.docid: 80188
negative_passages.text: There are infinitely many irreducible polynomials in $\Bbb{F}_p[X]$