16 problems

Richmond–Szekeres conjecture. The coefficients satisfy

Let … The sign patterns are coefficient patterns in the displayed order. Schlosser and Zhou's conjecture. For $\delta=1$, the coefficients of $Q_{10}(q)^{\delta}$ exhibit…

Schlosser's conjecture. If $\delta$ is real and

Assume $|q|<1$ and $z\ne0$. Here $E(q):=\prod_{k=1}^{\infty}(1-q^k)$, $(z;q)_\infty:=\prod_{k=0}^{\infty}(1-zq^k)$, and $[z;q]_\infty:=(z;q)_\infty(q/z;q)_\infty$. The notation…

Rational-factor conjecture. At $\alpha=-q^\ell t^{1/2}$,

Pfaffian product conjecture. At $\alpha=q^{1/2}t^{1/2}$,

Product-formula conjecture. The following identities hold:

Let … The preceding discussion suggests that this infinite product defines the integrand below. Cosine-product integral conjecture. … This is presented as a numerical conjecture mo…

Let $\mathcal{Z}$ be the string partition function, let $x$ be the string coupling parameter, and let $F_0^{(0)}$ and $F_1^{(0)}$ be the classical genus-zero and genus-one potentia…

The general $l^{\infty}$-product estimate. Is the estimate

Baruah–Sarma sign conjecture. For all integers $n\geq 0$,

Wang's conjecture. For any positive integers $t$ and $m$, the sequence of coefficients $\{c_t^{(m)}(n)\}_{n\geq 0}$ is ultimately periodic in sign, with least period of sign divisi…

Badziahin's denominator-degree conjecture. For all the other pairs $(u,v)\in\mathbb{Z}^2$, one has

Let $x=(x_1,x_2,\ldots)$ be an infinite set of variables, and let $\kappa^{(1)}_{\lambda}(q,t)$ and $\kappa^{(2)}_{\lambda}(q,t)$ be the limiting coefficients defined in the source…

Throughout, use the $q$-series notation … and $(A,B,\ldots,C;q)_\infty:=(A;q)_\infty(B;q)_\infty\cdots(C;q)_\infty$. Seo–Yee's nonnegativity conjecture. The series expansion of … h…

Diagonal residue product conjecture. We have