3 problems

Let $p,q,t\in\mathbb C$ satisfy $M<|t|^{n+1}<1$. For fixed $w\in\mathbb T^n$, let $C_w$ be a contour inside the annulus … for infinitesimally small positive $\epsilon$, with the po…

Let $n$ be a positive integer. Let $z_i$, $i=1,\dots,n$, $t_k$, $k=1,\dots,n+1$, and $f_j$, $j=1,\dots,n+2$, be independent complex variables, and set … With…

Let $\mathcal{I}(b,\beta)$ be a general Romelsberger index, and let the hyperbolic limit mean $\beta\to0^+$ with $b\in]0,\infty[$ fixed. The estimate in question is understood with…