Non-vanishing mod $p$ of theta lifts for (O_{2n+1},Mp_{4n})

Xiaoyu Zhang

We establish the non-vanishing mod $p$ of certain global theta lifts from a compact orthogonal group ${\mathrm{O}}_{2n+1}$ over $\mathbb{Q}$ to a metaplectic group ${\mathrm{Mp}}_{4n}$…