# Questions tagged [polynomials]

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.

**10**

**1**answer

### Cycling through the Zeta Garden: Zeta functions for graphs, cycle index polynomials, and determinants

**10**

**2**answers

### Riemann zeta function at positive integers and an Appell sequence of polynomials related to fractional calculus

**202**

**10**answers

### If $f$ is infinitely differentiable then $f$ coincides with a polynomial

**365**

**15**answers

### Why do roots of polynomials tend to have absolute value close to 1?

**44**

**5**answers

### The resultant and the ideal generated by two polynomials in $\mathbb{Z}[x]$

**13**

**2**answers

### About irreducible trinomials

**69**

**9**answers

### Irreducibility of polynomials in two variables

**91**

**11**answers

### Can a non-surjective polynomial map from an infinite field to itself miss only finitely many points?

**16**

**2**answers

### Conditions for smooth dependence of the eigenvalues and eigenvectors of a matrix on a set of parameters

**6**

**1**answer

### If $f,g \in D[x,y]$ are algebraically dependent over $D$, then $f,g \in D[h]$ for some $h\in D[x,y]$?

**8**

**1**answer

### Loday's characterization and enumeration of faces of associahedra (Stasheff polytopes)

**125**

**0**answers

### Why polynomials with coefficients $0,1$ like to have only factors with $0,1$ coefficients?

**64**

**6**answers

### How to recognise that the polynomial method might work

**28**

**5**answers

### Criteria to determine whether a real-coefficient polynomial has real root?

**29**

**6**answers

### Bass' stable range of $\mathbf Z[X]$

**36**

**2**answers

### A question on maps from $\mathbb{Z}/p\mathbb{Z}$ to itself

**19**

**1**answer

### Symmetric polynomial from graphs

**19**

**3**answers

### Cyclotomic polynomials: $\Phi_n(p)$ is like $p^{\phi(n)}$ for big enough $p$, right?

**2**

**2**answers

### Can one estimate the distribution of eigenvalues of a matrix by its Cauchy/Stieltje transform?

**6**

**2**answers

### Unexpectedly prime rich cubic polynomial

**16**

**4**answers

### Finite interpolation by a nondecreasing polynomial

**8**

**1**answer

### Is the restriction of a graded automorphism linearizable in characteristic zero?

**5**

**1**answer

### $f,g \in \mathbb{Z}[x,y]$ satisfying: $\operatorname{Jac}(f,g)=0$ and $f,g \notin \mathbb{Z}[h]$ for every $h \in \mathbb{Z}[x,y]$?

**2**

**1**answer

### Relating face polytopes of permutohedra to integer partitions

**71**

**7**answers

### Roots of truncations of $ e^x - 1$

**31**

**1**answer

### Integers not represented by $ 2 x^2 + x y + 3 y^2 + z^3 - z $

**38**

**4**answers

### The sum of squared logarithms conjecture

**21**

**3**answers

### Using higher-order Bring radicals to solve arbitrary polynomials

**16**

**1**answer

### Is $x^{n}-x-1$ irreducible?

**27**

**4**answers

### Distribution of roots of complex polynomials

**17**

**1**answer

### Density of polynomials in $C^k(\overline\Omega)$

**16**

**6**answers

### What's an example of a transcendental power series?

**25**

**2**answers

### Are these two new ways of representing odd zeta values as integrals known?

**23**

**1**answer

### Hilbert's Theorem on $L_2$ norm of polynomials in $\mathbb{Z}[X]$ - Explicit construction and a converse?

**17**

**3**answers

### $\prod_k(x\pm k)$ in binomial basis?

**24**

**5**answers

### Monic polynomial with integer coefficients with roots on unit circle, not roots of unity?

**8**

**1**answer

### polarization formula for homogeneous polynomials

**4**

**1**answer

### Reduced resultant of monic polynomials

**16**

**1**answer

### Cyclotomic polynomials 2

**8**

**7**answers

### Old question of Serre on discriminants of a sequence of polynomials

**8**

**6**answers

### Getting a bound on the coefficients of the factor polynomial

**4**

**1**answer

### Why are all these families of polynomials finally log-concave?

**25**

**2**answers

### Are there irreducible polynomials with all zeros on two concentric circles?

**7**

**2**answers

### Moment matching: construction of a mixture of Gaussian distribution with lower moments identical to Gaussian

**7**

**3**answers

### Rational exponential expressions

**6**

**1**answer

### An equivalence relation on the space of polynomials in one complex variable

**5**

**1**answer

### Irreducible polynomial $p_{n}(x)=\sum_{k=0}^{n}\frac{x^k}{k!}$ for all positive integers $n$

**5**

**0**answers

### Log-concave polynomial is a log-concave function?

**4**

**1**answer

### A discrete operator begets even/odd polynomials

**3**

**0**answers