5 problems

Let $v_{l,k}(f)$ be the finite-level local factor and let $v_l(f)$ be its limit. Power-saving local-factor approximation. There is a constant $\delta>0$ such that … This conjecture…

Let $v_{l,k}(f)$ be the normalized proportion of matrices in $\operatorname{GSp}_{2g}(\mathbb{Z}/l^k\mathbb{Z})$ having the prescribed polynomial data $f$, and let $v_l(f)$ be its…

Broadhurst50Roberts' local conductor conjecture. Based on numerical data, one has

Braverman–Kazhdan's zeta-integral conjecture. For every $f\in {\mathcal {S}}_{\rho}(G)$ and every $\varphi\in {\mathcal {C}}(\pi)$, the integral $Z(s,f,\varphi)$ is absolutely conv…

Monodromy conjecture. The Hasse–Weil local factor $\zeta(X,s)$ is independent of the choice of the prime $\ell$ not dividing $q$. This is conjectured as a consequence of the monodr…