# Tagged Questions

This tag is used for both basic and advanced questions on polynomials in any number of variables. Including, but not limited to: solving for roots, factoring, checking for irreducibility. This tag is rarely used as the only tag for a question.

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### Polynomial in the components of the curvature tensor

Consider a closed Riemannian manifold $(M,g)$ of dimension n and let $K(t,x,y)$ be its heat kernel. Then it is known that the heat kernel has an asymptotic expansion as $t\downarrow 0$: ...
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### Can a hermitian, rational polynomial have non-zero odd and real coefficients in the numerator/denominator?

Assume that we have a rational polynomial of the form: $$\chi\left(\omega\right)=\frac{\sum_{n=0}\left(c_n+ic_n^{\dagger}\right)\omega^{n}}{\sum_{n=0}\left(d_n+id_n^{\dagger}\right)\omega^{n}}$$ ...
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### Decomposition of an algebraic number into a sum or product of algebraic numbers with smaller degree

An algebraic number can be identified by its minimal polynomial together with isolating intervals with rational bounds for its real and imaginary parts. The degree of an algebraic number is the degree ...
### Divergence of squared sum of Chebyshev Polynomials $\equiv L+R$ has empty point spectrum
The Chebyshev Polynomials of the second kind $U_n$ are the solutions of the differential equation $$(1-x^2)U_n''(x)-3xU_n'(x)+n(n+2)U_n(x)=0$$ Alternatively they are defined inductively: U_0(x)=1 ...
### Is there a polynomial such that $F(p)$ is always divisible by a prime greater than $p$?
Is there an integer-valued polynomial $F$ such that for all prime $p$, $F(p)$ is divisible by a prime greater than $p$? For example, $n^2+1$ doesn't work, since $7^2+1 = 2 \cdot 5^2$. I can see that ...