5 problems

Let $\lambda$ be a positive real number and let $n$ be an integer with $n\geqslant 2$. Let $S(x)$ be a nonnegative nondecreasing function on $[0,+\infty)$. If … for every…

Transformation conjecture. The function $F(\alpha)$ also satisfies

Let ${\Bbb D}(X)$ be the algebra of $G$-invariant differential operators on $X$, viewed as holomorphic differential operators on $X_\mathbb{C}$. Let $\mathcal{O}(D_+)_\lambda$ deno…

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 $H(\delta)=\{z\in\mathbb{C}\mid\operatorname{Re}(z)\ge -\delta\}$ for some $0<\delta<1$. Define polynomials by $P_1(x)=1$, $P_2(x)=x$, and … for $m>2$. Let $g(z)$ be analytic o…