4 problems

Leading-term conjecture. The Taylor expansion of $Y_M(s)$ at $s=0$ satisfies

Truncation invariance conjecture. For every integer $k$ with $0\leqslant k<\operatorname{rk}(M)$,

Nestoridis's conjecture. The set $S(\Omega)$ is a dense $G_\delta$ subset of $\mathcal{H}(\Omega)$.

Normalize the limiting functions $f$ and $\widehat f$ so that $f(0)=\widehat f(0)=1$, and consider their Taylor expansions at $0$. Rational quadratic-coefficient conjecture. For…