Tsaltas, K. and Jarvis, A.F. (2019) Descending congruences of theta lifts on GSp4. Journal of Number Theory, 199. pp. 251-288. ISSN 0022-314X
Abstract
We study the question of when a congruence between two theta lifts on descends to a congruence on modular forms on over a quadratic field. In order to accomplish that, we use the theory of the local theta correspondence between similitude orthogonal groups and the similitude symplectic group , together with a classification for the degeneration modulo a prime of conductors for the L-parameters of irreducible admissible representations of over a non-archimedean local field. We explain that this is unlikely to be used in conjunction with existing results on congruences for to deduce a theory of congruences over imaginary quadratic fields. On the other hand, we prove a result which does give some such congruence results by twisting.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier. This is an author produced version of a paper subsequently published in Journal of Number Theory. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Siegel modular forms; Congruences; Theta lifts |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 14 Dec 2018 16:28 |
Last Modified: | 24 Nov 2021 10:56 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jnt.2018.11.012 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:140012 |