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Let E/L be a real quadratic extension of number fields. We construct an explicit map from an irreducible cuspidal automorphic representation of \(\mathop \textrm{GL}(2,E)\) which contains a Hilbert modular form with \(\Gamma _0\) level to an irreducible automorphic representation of \(\mathop \textrm{GSp}(4,L)\) 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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An Explicit Theta Lift to Siegel Paramodular Forms

  • 会议论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年

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  • Jennifer Johnson-Leung,
  • Nina Rupert

摘要

Let E/L be a real quadratic extension of number fields. We construct an explicit map from an irreducible cuspidal automorphic representation of \(\mathop \textrm{GL}(2,E)\) which contains a Hilbert modular form with \(\Gamma _0\) level to an irreducible automorphic representation of \(\mathop \textrm{GSp}(4,L)\) 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.