An explicit Waldspurger formula for Hilbert modular forms
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- by Nicolás Sirolli and Gonzalo Tornaría PDF
- Trans. Amer. Math. Soc. 370 (2018), 6153-6168
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.References
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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
- MR Author ID: 1067127
- ORCID: 0000-0002-0603-4784
- Email: nsirolli@dm.uba.ar
- Gonzalo Tornaría
- Affiliation: Centro de Matematica, Universidad de la República, 11400 Montevideo, Uruguay
- Email: tornaria@cmat.edu.uy
- 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
- © Copyright 2018 by 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
- MathSciNet review: 3814327