3 problems

For positive integers $k$ and $\ell$, define the polynomial … where $B_m$ denotes the $m$th Bernoulli number. Maji–Sarkar conjecture. All the non-real zeros of $R_{k,\ell}(x)$ lie…

Let $Q_n(x,y,z,t)$ be defined recursively by … For the Ramanujan operads $\operatorname{Ram}(\{1,2,\ldots,n\})$, write the homogeneous component of degree $(i,j)$ for the component…

Conjecture on the zeros of $R_{2k+1,p}$. The only real root of $R_{2k+1,p}(z)$ is $z=0$, with multiplicity $2$; moreover, its non-real roots are simple and lie on the circle…