Navegar

Colección

Datos Estadísticas

Artículo

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:

Given a weight 2 and level p2 modular form f, we construct two weight 3/2 modular forms (possibly zero) of level 4 p2 and non-trivial character mapping to f via the Shimura correspondence. Then we relate the coefficients of the constructed forms to the central value of the L-series of certain imaginary quadratic twists of f. Furthermore, we give a general framework for our construction that applies to any order in definite quaternion algebras, with which one can, in principle, construct weight 3/2 modular forms of any level, provided one knows how to compute ideal classes representatives. © 2006 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:Shimura correspondence for level p2 and the central values of L-series
Autor:Pacetti, A.; Tornaría, G.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria, CP 1428 Buenos Aires, Argentina
Department of Mathematics, University of Texas at Austin, Austin, TX 78712, United States
Palabras clave:L-series; Real twists; Shimura correspondence
Año:2007
Volumen:124
Número:2
Página de inicio:396
Página de fin:414
DOI: http://dx.doi.org/10.1016/j.jnt.2006.10.011
Título revista:Journal of Number Theory
Título revista abreviado:J. Number Theory
ISSN:0022314X
CODEN:JNUTA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022314X_v124_n2_p396_Pacetti

Referencias:

  • Atkin, A., Lehner, J., Hecke operators on Γ0 (m) (1970) Math. Ann., 185, pp. 134-160
  • Böcherer, S., Schulze-Pillot, R., On a theorem of Waldspurger and on Eisenstein series of Klingen type (1990) Math. Ann., 288, pp. 361-388
  • Böcherer, S., Schulze-Pillot, R., The Dirichlet series of Koecher and Maass and modular forms of weight frac(3, 2) (1992) Math. Z., 209 (2), pp. 273-287
  • Bump, D., Friedberg, S., Hoffstein, J., Nonvanishing theorems for L-functions of modular forms and their derivatives (1990) Invent. Math., 102, pp. 543-618
  • Gross, B., Heights and special values of L-series (1986) Conference Proceedings of the CMS, 7, pp. 115-187. , Amer. Math. Soc
  • Llorente, P., Correspondencia entre formas ternarias enteras y órdenes cuaterniónicos (2000) Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.), 94 (3), pp. 397-416
  • Pacetti, A., Rodriguez-Villegas, F., Computing weight 2 modular forms of level p2 (2005) Math. Comp., 74, pp. 1545-1557
  • Pizer, A., Theta series and modular forms of level p2 M (1980) Compos. Math., 40 (2), pp. 177-241
  • Shimura, G., On modular forms of half integral weight (1971) Ann. of Math., 97, pp. 440-481
  • Tornaría, G., (2004) Data about the central values of the L-series of (imaginary and real) quadratic twists of elliptic curves, , http://www.ma.utexas.edu/users/tornaria/cnt/
  • Ueda, M., The decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators (1988) J. Math. Kyoto Univ., 28 (3), pp. 505-555
  • Ueda, M., On twisting operators and newforms of half-integral weight (1993) Nagoya Math. J., 131, pp. 135-205
  • Waldspurger, J.-L., Sur les coefficients de Fourier des formes modulaires de poids demi-entier (1981) J. Math. Pures Appl., 60 (4), pp. 375-484

Citas:

---------- APA ----------
Pacetti, A. & Tornaría, G. (2007) . Shimura correspondence for level p2 and the central values of L-series. Journal of Number Theory, 124(2), 396-414.
http://dx.doi.org/10.1016/j.jnt.2006.10.011
---------- CHICAGO ----------
Pacetti, A., Tornaría, G. "Shimura correspondence for level p2 and the central values of L-series" . Journal of Number Theory 124, no. 2 (2007) : 396-414.
http://dx.doi.org/10.1016/j.jnt.2006.10.011
---------- MLA ----------
Pacetti, A., Tornaría, G. "Shimura correspondence for level p2 and the central values of L-series" . Journal of Number Theory, vol. 124, no. 2, 2007, pp. 396-414.
http://dx.doi.org/10.1016/j.jnt.2006.10.011
---------- VANCOUVER ----------
Pacetti, A., Tornaría, G. Shimura correspondence for level p2 and the central values of L-series. J. Number Theory. 2007;124(2):396-414.
http://dx.doi.org/10.1016/j.jnt.2006.10.011