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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Detalles Bibliográficos
Autores principales: Pacetti, A., Tornaría, G.
Formato: JOUR
Materias:
L-series
Real twists
Shimura correspondence
Acceso en línea: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 todo:paper_0022314X_v124_n2_p396_Pacetti
record_format dspace
spelling todo:paper_0022314X_v124_n2_p396_Pacetti2023-10-03T14:31:05Z Shimura correspondence for level p2 and the central values of L-series Pacetti, A. Tornaría, G. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Pacetti, A.
Tornaría, G.
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.
format JOUR
author Pacetti, A.
Tornaría, G.
author_facet Pacetti, A.
Tornaría, G.
author_sort Pacetti, A.
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
url http://hdl.handle.net/20.500.12110/paper_0022314X_v124_n2_p396_Pacetti
work_keys_str_mv AT pacettia shimuracorrespondenceforlevelp2andthecentralvaluesoflseries
AT tornariag shimuracorrespondenceforlevelp2andthecentralvaluesoflseries
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