4 problems

Krasikov's stronger conjecture. One has

Simple-zero conjecture. For any partitions $\lambda$ and $\mu$, take $\alpha>-1$ and $\beta>m_1$ such that the stated conditions are satisfied. If $\lambda$ is an even partition, t…

Let $\alpha,\beta\in(0,\infty)\setminus\mathbb{N}$, and let $F_n^{(\alpha,\beta),\delta}(t)$ denote the Jacobi-polynomial integral defined earlier in the paper. For $t\in(0,\pi]$ a…

Jacobi zero-preservation conjecture. If $\alpha$ and $\beta$ are non-negative integers, then $T_{\alpha,\beta}$ preserves the set of polynomials whose zeros lie only in $(-1,1)$. T…