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Transactions of the American Mathematical Society

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An explicit Waldspurger formula for Hilbert modular forms


Authors: Nicolás Sirolli and Gonzalo Tornaría
Journal: Trans. Amer. Math. Soc. 370 (2018), 6153-6168
MSC (2010): Primary 11F67, 11F41, 11F37
DOI: https://doi.org/10.1090/tran/7112
Published electronically: March 20, 2018
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Abstract:

We describe a construction of preimages for the Shimura map on Hilbert modular forms and give an explicit Waldspurger type formula relating their Fourier coefficients to central values of twisted $ L$-functions. Our construction is inspired by that of Gross and applies to any nontrivial level and arbitrary base field, subject to certain conditions on the Atkin-Lehner eigenvalues and on the weight.


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Additional Information

Nicolás Sirolli
Affiliation: Departamento de Matemática, Oficina 2096, Facultad de Ciencias Exactas y Naturales (C1428EGA) Pabellón I, Ciudad Universitaria, Ciudad Autónoma de Buenos Aires, Argentina
Email: nsirolli@dm.uba.ar

Gonzalo Tornaría
Affiliation: Centro de Matematica, Universidad de la República, 11400 Montevideo, Uruguay
Email: tornaria@cmat.edu.uy

DOI: https://doi.org/10.1090/tran/7112
Keywords: Waldspurger formula, Hilbert modular forms, Shimura correspondence
Received by editor(s): March 30, 2016
Received by editor(s) in revised form: October 26, 2016
Published electronically: March 20, 2018
Additional Notes: The first author was fully supported by the ANII under grant code PD_NAC_2013_1_11010
Article copyright: © Copyright 2018 by Nicolás Sirolli and Gonzalo Tornaría

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