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Results tagged with polynomials
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user 1004
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.
25
votes
Polynomial representing all nonnegative integers
Polynomials of degree less than four can be quickly dismissed. Then, assuming $f$ has degree $2n$, look at the leading order terms $f_{2n}$, which is a homogeneous polynomial of degree $2n$. … So, polynomials such as \eqref{47389_1} appear unlikely to do what we want, but proving this seems to be very difficult. …
- 17.1k
22
votes
Accepted
When are complex polynomial maps almost surjective?
Being algebraically independent is indeed a necessary and sufficient condition for the image of $f$ to be dense.
As $f\colon\mathbb{C}^n\to\mathbb{C}^n$ is regular, its image is constructible and, in …
- 17.1k
15
votes
Accepted
Distribution of roots of complex polynomials
Hence the sequence of polynomials $f_n=c_0+c_1X+\cdots+c_nX^n$ converge uniformly on the ball of radius $r$ (with probability 1). …
- 17.1k