6 problems

Let $f$ be an algebraic function analytic at $\infty$, and let $[n/n]$ denote its diagonal Padé approximants. A spurious pole is a pole of a Padé approximant in the sense defined i…

Consider the $[P/P]$-Padé approximant $R_P(z)=T_P(z)/Q_P(z)$, where $T_P$ and $Q_P$ have degree $P$ and are computed from the first $2P+1$ Taylor coefficients of $f$. Let $t$ denot…

Coefficient matching conjecture. In the limit as $m$ tends to infinity, the continued fraction $g_m(n)$ agrees with $B(n)$; equivalently, their numerator sequences satisfy

Let $F\in\mathcal F_f$ be an admissible compact set for $f$, and let $\{\Omega_n\}$ be an interpolation table disjoint from $F$. Assume that the limiting density $\omega$ in the in…

Strong asymptotics conjecture.

Let ${\bf f}=(f_1,\ldots,f_d)$ and ${\bf m}=(m_1,\ldots,m_d)\in\mathbb{Z}_+^d\setminus\{{\bf 0}\}$, and suppose that the denominator $Q_{n,\bf m}$ is unique for all sufficiently la…