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Abstract:

Let K be a real quadratic field and OK its ring of integers. Let Γ be a congruence subgroup of SL2(OK) and M(k1,k2)(Γ) be the finite dimensional space of Hilbert modular forms of weight (k1, k2) for Γ. Given a form f(z) ∈ M(k1,k2)(Γ), how many Fourier coefficients determine it uniquely in such space? This problem was solved by Hecke for classical forms, and Sturm proved its analogue for congruences modulo a prime ideal. The present article solves the same problem for Hilbert modular forms over K. We construct a finite set of indices (which depends on the cusps desingularization of the modular surface attached to Γ) such that the Fourier coefficients of any form in such set determines it uniquely. © 2016 American Mathematical Society.

Registro:

Documento: Artículo
Título:Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
Autor:Gil, J.I.B.; Pacetti, A.
Filiación:ICMAT (CSIC-UAM-UCM-UC3), C/ Nicolás Cabrera 13-15, Madrid, 28049, Spain
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Argentina
Año:2017
Volumen:86
Número:306
Página de inicio:1949
Página de fin:1978
DOI: http://dx.doi.org/10.1090/mcom/3187
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v86_n306_p1949_Gil

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Citas:

---------- APA ----------
Gil, J.I.B. & Pacetti, A. (2017) . Hecke and sturm bounds for Hilbert modular forms over real quadratic fields. Mathematics of Computation, 86(306), 1949-1978.
http://dx.doi.org/10.1090/mcom/3187
---------- CHICAGO ----------
Gil, J.I.B., Pacetti, A. "Hecke and sturm bounds for Hilbert modular forms over real quadratic fields" . Mathematics of Computation 86, no. 306 (2017) : 1949-1978.
http://dx.doi.org/10.1090/mcom/3187
---------- MLA ----------
Gil, J.I.B., Pacetti, A. "Hecke and sturm bounds for Hilbert modular forms over real quadratic fields" . Mathematics of Computation, vol. 86, no. 306, 2017, pp. 1949-1978.
http://dx.doi.org/10.1090/mcom/3187
---------- VANCOUVER ----------
Gil, J.I.B., Pacetti, A. Hecke and sturm bounds for Hilbert modular forms over real quadratic fields. Math. Comput. 2017;86(306):1949-1978.
http://dx.doi.org/10.1090/mcom/3187