Berger, T. orcid.org/0000-0002-5207-6221, Klosin, K. and Kramer, K. (2014) On higher congruences between automorphic forms. Mathematical Research Letters, 21 (1). pp. 71-82. ISSN 1073-2780
Abstract
We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform \pi_0 we prove an exact relation between the p-adic valuation of the order of C and the sum of the exponents of p-power congruences between the Hecke eigenvalues of \pi_0 and other automorphic forms. We apply this result to several situations including the congruences described by Mazur's Eisenstein ideal.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © by International Press of Boston, Inc. All rights reserved. |
Keywords: | math.NT; math.NT; 11F33 |
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: | 17 May 2016 13:49 |
Last Modified: | 26 Jun 2016 16:22 |
Published Version: | http://dx.doi.org/10.4310/MRL.2014.v21.n1.a5 |
Status: | Published |
Publisher: | International Press of Boston |
Refereed: | Yes |
Identification Number: | 10.4310/MRL.2014.v21.n1.a5 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:97963 |