Birkbeck, C;
(2019)
Slopes of Overconvergent Hilbert Modular Forms.
Experimental Mathematics
10.1080/10586458.2018.1538909.
(In press).
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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.
| Type: | Article |
|---|---|
| Title: | Slopes of Overconvergent Hilbert Modular Forms |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/10586458.2018.1538909 |
| Publisher version: | http://doi.org/10.1080/10586458.2018.1538909 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10069200 |
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