query: An entire and one-to-one function must be of the form AZ+B, A non-zero. How to rule out higher degree polynomials in z?
positive_passages.docid: 10181
positive_passages.text: Entire one-to-one functions are linear
negative_passages.docid: 137218
negative_passages.text: Does there exist a polynomial $f(x)$ with real coefficients such that $f(x)^2$ has fewer nonzero coefficients than $f(x)$?
negative_passages.docid: 139614
negative_passages.text: Polynomial bounded real part of an entire function
negative_passages.docid: 146506
negative_passages.text: If a complex function $f$ is Entire, and there exist $k,R > 0$, $n \in N$ such that $|f(z)| > k|z|^n$ for all $|z| > R$, then f is a polynomial.
negative_passages.docid: 100862
negative_passages.text: Polynomials with rational zeros
negative_passages.docid: 40502
negative_passages.text: The Degree of Zero Polynomial.
negative_passages.docid: 74245
negative_passages.text: Characterizing non-constant entire functions with modulus $1$ on the unit circle
negative_passages.docid: 20907
negative_passages.text: Entire function, Liouville and zeroes
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 68071
negative_passages.text: 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 $n$.
negative_passages.docid: 37084
negative_passages.text: Do two distinct level sets determine a non-constant complex polynomial?
negative_passages.docid: 129109
negative_passages.text: Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
negative_passages.docid: 81063
negative_passages.text: If $p$ is a polynomial, then either $\,p(z)=z^n\,$ or $\,\max_{|z|=1}|p(z)|>1$.
negative_passages.docid: 151729
negative_passages.text: Existence of a unique polynomial
negative_passages.docid: 123249
negative_passages.text: An analytic function $f$ on $|z|<1$ with $\sup_{|z|<1} |f(z)|=1$ and $|f(0)|=\frac{1}{2}$ has no zeros in $|z|<\frac{1}{2}$
negative_passages.docid: 140978
negative_passages.text: Real domain and range function to find all functions with nonzero x.
negative_passages.docid: 40014
negative_passages.text: A polynomial that is zero on an open set