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

TL;DR

This paper proves that certain global theta lifts from an orthogonal group to a metaplectic group do not vanish modulo a prime p, under mild conditions, advancing understanding of automorphic forms and theta correspondence.

Contribution

It establishes the non-vanishing modulo p of specific global theta lifts between orthogonal and metaplectic groups, a novel result in the theory of automorphic forms.

Findings

Non-vanishing mod p of theta lifts proven

Conditions for non-vanishing are mild and explicit

Advances understanding of automorphic forms and theta correspondence

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.