6 problems

Let $\theta(q,x)$ be the partial theta function. For $q\in(0,1)$, the zeros are complex-conjugation invariant, so nonreal zeros occur in complex conjugate pairs; for each…

Uniqueness conjecture. The spectral values $\tilde{q}_1$ and $v_{\pm}$ are the only spectral values of $\theta$ for

Let … where $\widetilde q\approx 0.3092493386$ is the positive threshold described in the source. Sokal's partial-theta problem. Is it true that all zeros of $\Theta_0(z;q)$ remain…

Berndt–Kim conjecture. For sufficiently large $n$, the coefficients $a_n$ have the same sign.

Iteration-convergence conjecture. If $0<q\leq\widetilde q$, then $\{f_j(x)\}$ converges uniformly on $[-1,0]$, together with all derivatives, to

Euler-transform coefficient conjecture. The sequence $(c_m)_{m=1}^{\infty}$ is strictly positive, increasing, strictly convex, and satisfies $\Delta^k c\geq0$ for $k=3,4$; explicit…