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On p-refined Friedberg–Jacquet integrals and the classical symplectic locus in the GL 2n eigenvariety

Barrera Salazar, Daniel; Graham, Andrew; Williams, Chris

On p-refined Friedberg–Jacquet integrals and the classical symplectic locus in the GL 2n eigenvariety Thumbnail


Authors

Daniel Barrera Salazar

Andrew Graham



Abstract

Friedberg–Jacquet proved that if π is a cuspidal automorphic representation of GL2n(A), then π is a functorial transfer from GSpin2n+1 if and only if a global zeta integral ZH over H=GLn×GLn is non-vanishing on π. We conjecture a p-refined analogue: that any P-parahoric p-refinement π~P is a functorial transfer from GSpin2n+1 if and only if a P-twisted version of ZH is non-vanishing on the π~P-eigenspace in π. This twisted ZH appears in all constructions of p-adic L-functions via Shalika models. We connect our conjecture to the study of classical symplectic families in the GL2n eigenvariety, and—by proving upper bounds on the dimensions of such families—obtain various results towards the conjecture.

Citation

Barrera Salazar, D., Graham, A., & Williams, C. (2025). On p-refined Friedberg–Jacquet integrals and the classical symplectic locus in the GL 2n eigenvariety. Research in Number Theory, 11(2), Article 51. https://doi.org/10.1007/s40993-025-00631-z

Journal Article Type Article
Acceptance Date Apr 14, 2025
Online Publication Date Apr 25, 2025
Publication Date 2025-06
Deposit Date Apr 26, 2025
Publicly Available Date Apr 28, 2025
Journal Research in Number Theory
Electronic ISSN 2363-9555
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 11
Issue 2
Article Number 51
DOI https://doi.org/10.1007/s40993-025-00631-z
Public URL https://nottingham-repository.worktribe.com/output/48176632
Publisher URL https://link.springer.com/article/10.1007/s40993-025-00631-z#
Additional Information Received: 4 March 2024; Accepted: 14 April 2025; First Online: 25 April 2025

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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/

Copyright Statement
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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