query: maximum of modulus polynomial of degree $n$ in circle of radius 1
positive_passages.docid: 149544
positive_passages.text: maximum of monic polynomial on unit circle is 1 implies $p(z)=z^n$
negative_passages.docid: 96127
negative_passages.text: Maximum of $|\sin(z)|$ as $\{z: |z| \leq 1 \} $
negative_passages.docid: 134342
negative_passages.text: Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.
negative_passages.docid: 113016
negative_passages.text: Remainder form of Taylor polynomial at $x_0$: $ \frac{1}{n!}f^{(n)}(x_0 +\theta(x-x_0))(x-x_0)^n$ with $\theta \to \frac{1}{n+1}$ as $ x \to x_0$
negative_passages.docid: 132059
negative_passages.text: Minimal polynomials and cyclic subspaces
negative_passages.docid: 26728
negative_passages.text: Coefficient of $n$th cyclotomic polynomial equals $-\mu(n)$
negative_passages.docid: 129834
negative_passages.text: Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
negative_passages.docid: 84374
negative_passages.text: Rational function with absolute value $1$ on unit circle
negative_passages.docid: 52594
negative_passages.text: Can all circles of radius $1/n$ be packed in a unit disk, excluding the circle of radius $1/1$?
negative_passages.docid: 147429
negative_passages.text: Set of points in $\mathbb{C}$ s.t. $z^{n-1} = \overline z$
negative_passages.docid: 26999
negative_passages.text: How is the degree of the minimal polynomial related to the degree of a field extension?
negative_passages.docid: 62958
negative_passages.text: Maximize $\mathrm{tr}(Q^TCQ)$ subject to $Q^TQ=I$
negative_passages.docid: 81790
negative_passages.text: Polynomial maximization: If $x^4+ax^3+3x^2+bx+1 \ge 0$, find the maximum value of $a^2+b^2$
negative_passages.docid: 42988
negative_passages.text: Complex polynomial and the unit circle
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: 100061
negative_passages.text: The Maximum possible order for an element $S_n$
negative_passages.docid: 151384
negative_passages.text: Summation of series involving binomial coefficients and polynomial of degree at most n-1