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

Abstract

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 ${\mathrm{Mp}}_{4n}$ over $\mathbb{Q}$ under mild conditions.

Final version, to appear in Forum Mathematicum