8 problems

Polynomial arctanh integral conjecture. For every nonzero integer polynomial $P$, one has

Let $n\in\mathbb{N}^*$, and consider the integral … For each $n$, let $C_{p,n}$ denote rational coefficients indexed by $1\leq p\leq n$. Integral representation conjecture. For eve…

Woronowicz-type integral representations.

Let $\mathbf G$ be a group of ${\rm GL}$-type, let $\phi:I_F^{(\ell)}\rightarrow {^{L}\mathbf G}$ be an admissible parameter, and choose an extension…

Let $\xi:{^{L}\mathbf G'}\rightarrow {^{L}\mathbf G}$ be as above, let $\phi'$ and $\phi=\xi\circ\phi'$ be the associated admissible parameters, and let…

Let $\mathbf{G}'$ and $\mathbf{G}$ be groups of ${\rm GL}$-type with an $L$-homomorphism $\xi:{^{L}\mathbf{G}'}\rightarrow {^{L}\mathbf{G}}$. Let…

Heun integral-representation conjecture. Heun's equation and its confluent equations, including the BHE, have no general integral representations of their solutions in terms of sim…

Whittaker's conjecture. Except in some trivial cases, no expressions of this kind exist.