Shimura correspondence for level p2 and the central values of L-series

Given a weight 2 and level p2 modular form f, we construct two weight 3/2 modular forms (possibly zero) of level 4 p2 and non-trivial character mapping to f via the Shimura correspondence. Then we relate the coefficients of the constructed forms to the central value of the L-series of certain imagin...

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Guardado en:
Detalles Bibliográficos
Publicado: 2007
Materias:
L-series
Real twists
Shimura correspondence
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022314X_v124_n2_p396_Pacetti
http://hdl.handle.net/20.500.12110/paper_0022314X_v124_n2_p396_Pacetti
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0022314X_v124_n2_p396_Pacetti
record_format dspace
spelling paper:paper_0022314X_v124_n2_p396_Pacetti2025-07-30T17:31:19Z Shimura correspondence for level p2 and the central values of L-series L-series Real twists Shimura correspondence Given a weight 2 and level p2 modular form f, we construct two weight 3/2 modular forms (possibly zero) of level 4 p2 and non-trivial character mapping to f via the Shimura correspondence. Then we relate the coefficients of the constructed forms to the central value of the L-series of certain imaginary quadratic twists of f. Furthermore, we give a general framework for our construction that applies to any order in definite quaternion algebras, with which one can, in principle, construct weight 3/2 modular forms of any level, provided one knows how to compute ideal classes representatives. © 2006 Elsevier Inc. All rights reserved. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022314X_v124_n2_p396_Pacetti http://hdl.handle.net/20.500.12110/paper_0022314X_v124_n2_p396_Pacetti
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic L-series
Real twists
Shimura correspondence
spellingShingle L-series
Real twists
Shimura correspondence
Shimura correspondence for level p2 and the central values of L-series
topic_facet L-series
Real twists
Shimura correspondence
description Given a weight 2 and level p2 modular form f, we construct two weight 3/2 modular forms (possibly zero) of level 4 p2 and non-trivial character mapping to f via the Shimura correspondence. Then we relate the coefficients of the constructed forms to the central value of the L-series of certain imaginary quadratic twists of f. Furthermore, we give a general framework for our construction that applies to any order in definite quaternion algebras, with which one can, in principle, construct weight 3/2 modular forms of any level, provided one knows how to compute ideal classes representatives. © 2006 Elsevier Inc. All rights reserved.
title Shimura correspondence for level p2 and the central values of L-series
title_short Shimura correspondence for level p2 and the central values of L-series
title_full Shimura correspondence for level p2 and the central values of L-series
title_fullStr Shimura correspondence for level p2 and the central values of L-series
title_full_unstemmed Shimura correspondence for level p2 and the central values of L-series
title_sort shimura correspondence for level p2 and the central values of l-series
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022314X_v124_n2_p396_Pacetti
http://hdl.handle.net/20.500.12110/paper_0022314X_v124_n2_p396_Pacetti
_version_ 1840321015017635840

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