An Explicit Theta Lift to Siegel Paramodular Forms

2025/01/15 by Johnson-Leung, Jennifer, Rupert, Nina
#11F46 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2501.09109

Abstract

Let E/L be a real quadratic extension of number fields. We construct an explicit map from an irreducible cuspidal automorphic representation of GL(2,E) which contains a Hilbert modular form with Γ₀ level to an irreducible automorphic representation of GSp(4,L) which contains a Siegel paramodular form and exhibit local data which produces a paramodular invariant vector for the local theta lift at every finite place, except when the local extension has wild ramification.

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