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Results tagged with polynomials
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user 24309
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.
3
votes
Accepted
Simple zeroes of complex polynomial $f(\cdot,a)$: condition on $P(a)=\operatorname{Res}_z(f,...
No, it's not true, as is shown by the polynomial $f(z,a):=(z-a)(z-1)^2$.
- 5,428
4
votes
Under what conditions does the Mittag-Leffler function ${E_{\alpha ,1}}(z),(0 < \alpha < 1)$...
EDIT: at the time of this answer the OP did not specify that the zero should be real.
The order (as an entire function) of $E_{\alpha,1}$ is $\frac{1}{\alpha}$. It so happens that entire functions wi …
- 5,428
3
votes
Polynomial vector field tangent to a given analytic simple closed curve
The answer is "no". In fact, it is still "no" for germs of curves : generically, a germ of an analytic curve $\gamma : (\mathbb R,0)\rightarrow (\mathbb R^2,0)$ is not tangent to any polynomial vector …
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11
votes
The holomorphic version of Galois theory
You can obtain this map as a section of the map $\sigma$ sending the $n$-tuple of the roots $(r_1,\ldots,r_n)$ to the coefficients of the polynomial using the symmetric polynomials, corresponding to the …
- 5,428
4
votes
1
answer
178
views
Effective bound on "Jacobian rank" for (regular) planar algebraic curves
(Here $\mathbb C[x,y]_{\leq k}$ is the vector space of polynomials of degree $\leq k$.) …
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