8 problems

Let $D_M$ be the differential operator defining the homogeneous Heun equation for $\Pi_M$, and let $d$ be the parameter specified by the relation referenced in the source. Polynomi…

Let $d_2(B)$ be the function associated with the Heun equation, the confluent Heun equation, and the reduced confluent Heun equation, and let $D_k$ and $D_k^{[j],(k+j+1)}$ denote t…

Netay's regularity conjecture. The curve $\Gamma_\ell^o$ is regular.

Consider the two double confluent Heun equations denoted in the source by equation … . Polynomial-versus-entire-solution conjecture. If equation … does not have an entire solution.…

Let $\xi_l(\lambda,\mu)=0$ be the explicit functional equation whose solutions give the constructed family of holomorphic solutions of the relevant double confluent Heun equation,…

The triangular-term sign conjecture. The ratio of these triangular terms is negative, in the source's notation meaning

Let $l\in\mathbb N$. Consider the two double confluent Heun equations in the source, with equation … by the substitution $l=1-n$. A polynomial solution means a nonzero solution of…

Let $l\geq 0$ be an integer, and let $\xi_l(\lambda,\mu)=0$ be the functional equation whose solutions produce entire solutions of the double confluent Heun equation associated wit…