3 problems

Zero distribution conjecture. $T^{(2)}_{n-1}(v)$ has one real zero $\zeta_{n-1}$ for $n$ even with $2\leq n\leq p_0-1$, and two real zeros $\zeta_{n-1}$ and $-\zeta'_{n-1}$ for $n$…

Determinant conjecture. As in the sine-Gordon model, the sinh-Gordon one-point functions in the fermionic basis satisfy

Let $u$ be sufficiently small, with $|u|\ll 1$, let $s$ be a positive integer, and let $a\in\{1,2,\dots,s\}$. For each positive integer $m$, let $T^{(a)}_{m}(v)$ denote the transfe…