9 problems

Let a spectral zeta function of a symmetric fractal have a product structure with a “polynomial” part and a “geometric” part, and suppose that poles of the polynomial part may be c…

Let $H$ be a Hamiltonian defining a quantum system, let $Z_H(t)$ be its partition function, and let $\widetilde{Z}_H(t)$ be its quasi-partition function as defined from the special…

NCHO quasi-partition-function conjecture. The following are expected: (1) $\widetilde{Z}_Q(t)=Z_Q(t)$; and (2), under (1), if

Let $H_n(s)$ be the function defined from the discrete-torus spectral zeta function by the asymptotic expansion … where … Here $\zeta(\Delta,s)$ is the spectral zeta function of th…

Let $\alpha\in\mathbb{N}$, let $\zeta_Q(s)$ be the Epstein zeta function associated with a real-valued positive definite $\alpha\times\alpha$ matrix $Q$, and let…

Functional-equation conjecture. For every $s\in\mathbb{C}$ with $0<\operatorname{Re}(s)<1$,

Let $F$ be the two-dimensional standard Sierpinski carpet, realized by two self-similar structures that yield the same Laplacian. Let $d_f$ be its fractal dimension and $d_w$ its w…

Let a generalized Sierpinski carpet have self-similar, possibly graph-directed, structures yielding the same Laplacian operator. Let $d_k$ denote the relevant dimensions, with…

Let $\Omega\subset\mathbb{R}^d$ be a domain with volume $|\Omega|$, and let $\zeta_{\mathrm{spec}}(\rho)=\sum_{j=1}^{\infty}\lambda_j^{-\rho}$ denote the spectral zeta function of…