Hecke and sturm bounds for Hilbert modular forms over real quadratic fields

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...

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Autores principales: Gil, J.I.B., Pacetti, A.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00255718_v86_n306_p1949_Gil
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spelling todo:paper_00255718_v86_n306_p1949_Gil2023-10-03T14:36:15Z Hecke and sturm bounds for Hilbert modular forms over real quadratic fields Gil, J.I.B. Pacetti, A. 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. Fil:Pacetti, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00255718_v86_n306_p1949_Gil
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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.
format JOUR
author Gil, J.I.B.
Pacetti, A.
spellingShingle Gil, J.I.B.
Pacetti, A.
Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
author_facet Gil, J.I.B.
Pacetti, A.
author_sort Gil, J.I.B.
title Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_short Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_full Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_fullStr Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_full_unstemmed Hecke and sturm bounds for Hilbert modular forms over real quadratic fields
title_sort hecke and sturm bounds for hilbert modular forms over real quadratic fields
url http://hdl.handle.net/20.500.12110/paper_00255718_v86_n306_p1949_Gil
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AT pacettia heckeandsturmboundsforhilbertmodularformsoverrealquadraticfields
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