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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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 |
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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 |
| work_keys_str_mv |
AT giljib heckeandsturmboundsforhilbertmodularformsoverrealquadraticfields AT pacettia heckeandsturmboundsforhilbertmodularformsoverrealquadraticfields |
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1807320448438894592 |