9 problems

Keith's conjecture. For $n\geq 0$,

Let $p$ be a positive integer, let $a$ be an index for the Mordell–Borel integrals $JS_{(p,a)}(t)$ and $JC_{(p,a)}(t)$, and let $q$ and $\widetilde{q}$ be the corresponding variabl…

Keith's conjecture. For every integer $n\geq 0$,

Let $p$ be an odd integer and let $J^{(A,p)}_j(t)$, $J^{(B,p)}_j(t)$, $J^{(C,p)}_j(t)$, and $J^{(D,p)}_j(t)$ denote the vectors of Mordell–Borel integrals defined in the source. Wr…

Conjectured congruences for $c_5$. The following congruences appear to hold:

Conjectured congruence classes. The following congruences appear to hold modulo $2$:

For $n\geq 0$, let $(x;q)_n=(1-x)(1-xq)\cdots(1-xq^{n-1})$ be the $q$-Pochhammer symbol, and let $\begin{bmatrix}n\\k\end{bmatrix}_q$ denote the $q$-binomial coefficient. For…

Dual-pair existence conjecture. There exists a unique dual pair. The supplied span ends before specifying the objects comprising the pair or the property that characterizes it, so…

Let $F_k(q)$ be defined by … Here $k\geq 1$, and $L_{\mathfrak{sp}(2k)}(\Lambda_0)$ denotes the suitably normalized level-one affine vertex algebra of type $C^{(1)}_k$, with charac…