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Paramodular forms in CAP representations of ${\rm GSp}(4)$

Volume 194 / 2020

Ralf Schmidt Acta Arithmetica 194 (2020), 319-340 MSC: 11F46, 11F70. DOI: 10.4064/aa180606-23-9 Published online: 1 April 2020


We explicitly determine the non-tempered local Arthur packets for ${\rm GSp} (4)$ of Howe–Piatetski-Shapiro type, Saito–Kurokawa type and Soudry type. As a consequence we show that Gritsenko lifts are the only paramodular forms that can occur in global CAP representations of ${\rm GSp} (4,\mathbb A _{\mathbb Q} )$.


  • Ralf SchmidtDepartment of Mathematics
    University of North Texas
    1155 Union Circle #311430
    Denton, TX 76203-5017, U.S.A.

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