Salvatore Mercuri
The p-adic L-function for half-integral weight modular forms
Mercuri, Salvatore
Authors
Abstract
The p-adic L-function for modular forms of integral weight is well-known. For certain weights the p-adic L-function for modular forms of half-integral weight is also known to exist, via a correspondence, established by Shimura, between them and forms of integral weight. However, we construct it here without any recourse to the Shimura correspondence, allowing us to establish its existence for all weights, including those exempt from the Shimura correspondence. We do this by employing the Rankin–Selberg method, and proving explicit p-adic congruences in the resultant Rankin–Selberg expression.
Citation
Mercuri, S. (2020). The p-adic L-function for half-integral weight modular forms. manuscripta mathematica, 161(1-2), 61-91. https://doi.org/10.1007/s00229-018-1085-1
Journal Article Type | Article |
---|---|
Acceptance Date | Oct 30, 2018 |
Online Publication Date | Nov 7, 2018 |
Publication Date | Jan 31, 2020 |
Deposit Date | Nov 23, 2018 |
Publicly Available Date | Nov 23, 2018 |
Journal | manuscripta mathematica |
Print ISSN | 0025-2611 |
Electronic ISSN | 1432-1785 |
Publisher | Springer |
Peer Reviewed | Peer Reviewed |
Volume | 161 |
Issue | 1-2 |
Pages | 61-91 |
DOI | https://doi.org/10.1007/s00229-018-1085-1 |
Related Public URLs | http://community.dur.ac.uk/salvatore.mercuri/padiclfun.pdf |
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Advance online version © The Author(s) 2018.<br />
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Published Journal Article
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