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Consider a degree four polynomial $$ f = a_4x^4 + a_3x^3 + a_2x^2 + a_1x+ a_0 \in \mathbb{R}[x] $$ with real coefficients. The discriminant $\Delta_f$ of $f$ is a homogeneous polynomials of degree six ...

Let $\mu$ be the Möbius function. It is well known that $\sum_{n|k} \mu(n) = 0$ for $k>1$. What could be said about the polynomials $R_k = \sum_{n|k} \mu(n) x^n$ for $x \in [0,1]$? There does not ...