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Results tagged with polynomials
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user 21724
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
7
votes
Accepted
Do the roots lie exactly on the Szego Curve or Approach it?
I assume you meant "if $z_n$ satisfies $f(n z_n)=0$ and if the sequence $z_n$ converge to a nonzero limit $z$ then $|z e^{1-z}|=1$ ".
Now, if $n z_n$ is a root of $f_n$ then $z_n$ is algebraic over $ …
- 7,249
5
votes
Accepted
Polynomials $P$ with integer roots near to $X^{\mathrm{deg}(P)}$
Thus the polynomials $P(X) = \prod_i (X-\alpha_i)$ and $Q(X) = \prod_i (X-\beta_i)$ are distinct, but satisfy $P(X) = Q(X) + O(X^{r-d})$. …
- 7,249
8
votes
Manifolds with polynomial transition maps
Let me develop Robert Bryant's answer :
if $M$ is a simply-connected manifold of dimension $n$ with a polynomial atlas, then there exists a local isomorphism $M \rightarrow \mathbb{R}^n$. Conversely, …
- 7,249
1
vote
Accepted
What are the fixed points of $\alpha^n-\mu_j$ for a fixed $j$?
Let $L$ be the line generated by $\underline{\mu} = (\mu_1,\dots,\mu_s)$ in $V = \mathbb{C}^s$, and consider a projection $p : V \rightarrow V$ onto $L$, with kernel $H$. Any polynomial function of th …
- 7,249