2 problems

Let $f\in k[x_1,\ldots,x_n]$, where $k=\mathbb R$ or $\mathbb C$, and let $Z_{f,\varphi}(s)$ be the associated complex version of the Archimedean zeta function. Let $b_f(s)$ denote…

Denef–Sargos conjecture. If $1/t_0\notin\mathbb{Z}$, then the pole order of $Z_f$ at $s=-1/t_0$ is equal to $\operatorname{codim}_{\mathbb{R}^n}\tau_0$ if and only if $\tau_0$ is s…