New York Journal of Mathematics
Volume 30 (2024), 1-23


David Loeffler

On local zeta-integrals for GSp(4) and GSp(4) x GL(2)

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Published: January 7, 2024.
Keywords: L-factors, zeta integrals.
Subject [2020]: 22E50.

We prove that Novodvorsky's definition of local L-factors for generic representations of GSp(4) x GL(2) is compatible with the local Langlands correspondence when the GL(2) representation is non-supercuspidal. We also give an interpretation in terms of Langlands parameters of the "exceptional" poles of the GSp(4) x GL(2) L-factor, and of the "subregular" poles of
GSp(4) L-factors studied in recent work of Rosner and Weissauer; and deduce consequences for Gan-Gross-Prasad type branching laws, either for reducible generic representations, or for irreducible but non-generic representations.


The author gratefully acknowledges the support of the Royal Society (University Research Fellowship "L-functions and Iwasawa theory") and the European Research Council through the Horizon 2020 Excellent Science programme (Consolidator Grant "Shimura varieties and the BSD conjecture", grant ID 101001051).

Author information

David Loeffler
Warwick Mathematics Institute, Zeeman Building
University of Warwick
Coventry CV4 7AL, UK
Current address: UniDistance Suisse
Schinerstrasse 18
3900 Brig, Switzerland