Artículo

Gil, J.I.B.; Pacetti, A."Hecke and sturm bounds for Hilbert modular forms over real quadratic fields" (2017) Mathematics of Computation. 86(306):1949-1978
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

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
Handle:http://hdl.handle.net/20.500.12110/paper_00255718_v86_n306_p1949_Gil
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

Referencias:

  • Baba, S., Chakraborty, K., Petridis, Y.N., On the number of Fourier coefficients that determine a Hilbert modular form (2002) Proc. Amer. Math. Soc, 130 (9), pp. 2497-2502. , (electronic). MR1900854
  • Chai, C.-L., Arithmetic minimal compactification of the Hilbert-Blumenthal moduli spaces (1990) Ann. of Math. (2), 131 (3), pp. 541-554. , MR1053489
  • Cohen, H., (1993) A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics, 138. , Springer-Verlag, Berlin,. MR1228206
  • Cox, D.A., (1989) Primes of the Form x2 + ny2: Fermat, Class Field Theory and Complex Multiplication, , A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York. MR1028322
  • Dieulefait, L., Pacetti, A., Schütt, M., Modularity of the Consani-Scholten quintic (2012) Doc. Math, 17, pp. 953-987. , With an appendix by José Burgos Gil and Pacetti. MR3007681
  • Freitag, E., (2003) Modular embeddings of hilbert modular surfaces, , http://www.rzuser.uni-heidelberg.de/~t91/index4.html
  • Garrett, P.B., (1990) Holomorphic Hilbert Modular Forms, , The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA. MR1008244
  • Goren, E.Z., (2002) Lectures on Hilbert Modular Varieties and Modular Forms, CRM Monograph Series, 14. , American Mathematical Society, Providence, RI,. With the assistance of Marc-Hubert Nicole. MR1863355
  • Hecke, E., (1970) Mathematische Werke (German), Vandenhoeck&Ruprecht, Göttingen, , Mit einer Vorbemerkung von B. Schoenberg, einer Anmerkung von Carl Ludwig Siegel, und einer Todesanzeige von Jakob Nielsen; Zweite durchgesehene Auflage. MR0371577
  • Hermann, C.F., Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper (German) (1987) Math. Ann, 277 (2), pp. 327-344. , MR886425
  • Hermann, C.F., Thetareihen und modulare Spitzenformen zu den Hilbertschen Modulgruppen reell-quadratischer Körper. II (German) (1989) Math. Ann, 283 (4), pp. 689-700. , MR990596
  • Katz, N.M., p-adic properties of modular schemes and modular forms, Modular Functions of One Variable, III (1972) Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 350, pp. 69-190. , Lecture Notes in Mathematics, Springer, Berlin. MR0447119 1973
  • Katsura, T., Ueno, K., On elliptic surfaces in characteristic p (1985) Math. Ann, 272 (3), pp. 291-330. , MR799664
  • Pappas, G., Arithmetic models for Hilbert modular varieties (1995) Compositio Math, 98 (1), pp. 43-76. , MR1353285
  • (2012) Bordeaux, PARI/GP, version 2.6.0, , http://pari.math.u-bordeaux.fr/
  • Rapoport, M., Compactifications de l'espace de modules de Hilbert-Blumenthal (French) (1978) Compositio Math, 36 (3), pp. 255-335. , MR515050
  • Shimura, G., (1994) Introduction to the Arithmetic Theory of Automorphic Functions, Publications of the Mathematical Society of Japan, 11. , Princeton University Press, Princeton, NJ,. Reprint of the 1971 original; Kanô Memorial Lectures, 1. MR1291394
  • van der Geer, G., Hilbert modular forms for the field Q(v6) (1978) Math. Ann, 233 (2), pp. 163-179. , MR0491516
  • van der Geer, G., (1988) Hilbert Modular Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 16. , Springer-Verlag, Berlin,. MR930101
  • van der Geer, G., Zagier, D., The Hilbert modular group for the field Q(v13) (1977) Invent. Math, 42, pp. 93-133. , MR0485704

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