Slopes of overconvergent Hilbert modular forms

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Birkbeck, Christopher ORCID: https://orcid.org/0000-0002-7546-9028 (2021) Slopes of overconvergent Hilbert modular forms. Experimental Mathematics, 30 (3). pp. 295-314. ISSN 1058-6458

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Abstract

We give an explicit description of the matrix associated to the Up operator acting on spaces of overconvergent Hilbert modular forms over totally real fields. Using this, we compute slopes for weights in the center and near the boundary of weight space for certain real quadratic fields. Near the boundary of weight space we see that the slopes do not appear to be given by finite unions of arithmetic progressions but instead can be produced by a simple recipe from which we make a conjecture on the structure of slopes. We also prove a lower bound on the Newton polygon of the Up.

Item Type:	Article
Additional Information:	Funding Information: This study was supported by Engineering and Physical Sciences Research Council (EP/N509577/1) The author would like to thank his supervisor Lassina Dembélé for his support and guidance. He would also like to thank Fabrizio Andreatta, David Hansen, Alan Lauder and Vincent Pilloni for interesting discussions and very useful suggestions. Lastly, this work is part of the authors thesis so I wish to thank my examiners Kevin Buzzard and David Loeffler, as well as the referee for their very useful comments and corrections. This study was supported by Engineering and Physical Sciences Research Council (EP/N509577/1).
Uncontrolled Keywords:	11f33,11f41,11y40,mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://www.scopus.com/inward/record.url?... https://discovery.ucl.ac.uk/id/eprint/10...
Depositing User:	LivePure Connector
Date Deposited:	15 May 2023 08:31
Last Modified:	07 Nov 2024 12:46
URI:	https://ueaeprints.uea.ac.uk/id/eprint/92052
DOI:	10.1080/10586458.2018.1538909

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