Abstract
We use the theta lifts between [Formula: see text] and [Formula: see text] to study the distinction problems for the pair [Formula: see text] where [Formula: see text] is a quadratic field extension over a nonarchimedean local field [Formula: see text] of characteristic zero and [Formula: see text] is a quaternion algebra. With a similar strategy, we give a conjectural formula for the multiplicity of distinction problem related to the pair [Formula: see text]
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