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The p-adic L-function for half-integral weight modular forms

Mercuri, Salvatore

The p-adic L-function for half-integral weight modular forms Thumbnail


Salvatore Mercuri


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.


Mercuri, S. (2020). The p-adic L-function for half-integral weight modular forms. manuscripta mathematica, 161(1-2), 61-91.

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
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Copyright Statement
Advance online version © The Author(s) 2018.<br /> This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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.

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