5 problems

Let $m,n\in \mathbb Z$ with $1\le m\le n-1$ and let $\delta\in \mathbb Z_{\ge0}$. For $x\in\mathbb C$ and $q\in\mathbb Z_{\ge0}$, write … Let $\what{n}{\alpha}{s}$ be the Mellin tr…

Let $I_{\lambda_0,f}(\lambda)$ denote the Mellin transform associated with the parameters $\lambda_0$, $f$, and $\lambda$, and let $q$ be the residue-field cardinality. Rationality…

Let $U\subset X$ be complex manifolds satisfying the conditions in Theorem. Let $\mathcal F\in D^b_c(X,A)$ be a constructible complex such that $\mathcal F|_U\neq 0$. Non-vanishing…

Self-duality conjecture. Under $\tau\mapsto1/\tau$ and $q\mapsto q/\tau$, it satisfies

Let … and define $M_{\widehat f}$ analogously for the Fourier transform $\widehat f$. Normalize the limiting functions by $f(0)=\widehat f(0)=1$. Mellin midpoint-value conjecture.…