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:

The purpose of this article is to show how the root number of a modular form changes by twisting in terms of the local Weil-Deligne representation at each prime ideal. As an application, we show how one can, for each odd prime p, determine whether a modular form (or a Hilbert modular form) with trivial nebentypus is either Steinberg, principal series or supercuspidal at p by analyzing the change of sign under a suitable twist. We also explain the case p = 2, where twisting, in general, is not enough. © 2012 American Mathematical Society.

Registro:

Documento: Artículo
Título:On the change of root numbers under twisting and applications
Autor:Pacetti, A.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, CP 1428, Buenos Aires, Argentina
Palabras clave:Local factors; Twisting epsilon factors
Año:2013
Volumen:141
Número:8
Página de inicio:2615
Página de fin:2628
DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11532-7
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v141_n8_p2615_Pacetti

Referencias:

  • Atkin, A.O.L., Lehner, J., Hecke operators on Γ0(m) (1970) Math. Ann., 185, pp. 134-160. , MR0268123 (42:3022)
  • Atkin, A.O.L., Li, W.C.W., Twists of newforms and pseudo-eigenvalues of W-operators (1978) Invent. Math., 48 (3), pp. 221-243. , MR508986 (80a:10040)
  • Bayer, P., Rio, A., Dyadic exercises for octahedral extensions (1999) J. Reine Angew. Math., 517, pp. 1-17. , MR1728550 (2001a:11191)
  • Carayol, H., Sur les représentations l-adiques associées aux formes modulaires de Hilbert (1986) Ann. Sci. École Norm. Sup., 19 (3), pp. 409-468. , MR870690 (89c:11083)
  • Davenport, H., Multiplicative number theory Graduate Texts in Mathematics, 74. , Springer-Verlag, New York, third edition, 2000. Revised and with a preface by Hugh L. Montgomery. MR1790423 (2001f:11001)
  • Deligne, P., Les constantes des équations fonctionnelles des fonctions (1973) Modular functions of one variable, 349, pp. 501-597. , II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Lecture Notes in Math., Springer, Berlin, MR0349635 (50:2128)
  • Dembélé, L., Explicit computations of Hilbert modular forms on Q(√5) (2005) Experiment. Math., 14 (4), pp. 457-466. , MR2193808 (2006h:11050)
  • Dembélé, L., An algorithm for modular elliptic curves over real quadratic fields (2008) Experiment. Math., 17 (4), pp. 427-438. , MR2484426 (2010a:11119)
  • Gérardin, P., Kutzko, P., Facteurs locaux pour GL(2) (1980) Ann. Sci. École Norm. Sup., 13 (3), pp. 349-384. , MR597744 (82i:22020)
  • Henniart, G., (1979) Représentations du groupe de Weil d'un corps local, 2. , Publications Mathématiques d'Orsay 79 [Mathematical Publications of Orsay 79]. Université de Paris-Sud Département de Mathématique, Orsay, With an English summary. MR551495 (80m:12016)
  • Hijikata, H., Pizer, A.K., Shemanske, T.R., The basis problem for modular forms on Γ0(N) (1989) Mem. Amer. Math. Soc., 82 (418), pp. 6+159. , MR960090 (90d:11056)
  • Li, W.C.W., On the representations of GL(2). I. ε-factors and n-closeness (1980) J. Reine Angew. Math., 313, pp. 27-42. , MR552460 (81h:10042a)
  • Loeffler, D., Weinstein, J., On the computation of local components of a newform (2012) Math. Comp., 81 (278), pp. 1179-1200. , MR2869056 (2012k:11064)
  • (2010) Computing ideal class representatives in quaternion algebras, , Ariel Pacetti and Nicolás Sirolli. Submitted, arXiv:1007.2821
  • Rio, A., Dyadic exercises for octahedral extensions (2006) J. Number Theory, 118 (2), pp. 172-188. , MR2223979 (2007c:11132)
  • Rohrlich, D.E., Variation of the root number in families of elliptic curves (1993) Compositio Math., 87 (2), pp. 119-151. , MR1219633 (94d:11045)
  • SAGE mathematics software, , http://www.sagemath.org/, version 4.5.2
  • Tate, J., Number theoretic background (1979) Amer. Math. Soc., pp. 3-26. , Automorphic forms, representations and Lfunctions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Providence, R.I., MR546607 (80m:12009)
  • 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/
  • Weil, A., Exercices dyadiques (1974) Invent. Math., 27, pp. 1-22. , MR0379445 (52:350)

Citas:

---------- APA ----------
(2013) . On the change of root numbers under twisting and applications. Proceedings of the American Mathematical Society, 141(8), 2615-2628.
http://dx.doi.org/10.1090/S0002-9939-2013-11532-7
---------- CHICAGO ----------
Pacetti, A. "On the change of root numbers under twisting and applications" . Proceedings of the American Mathematical Society 141, no. 8 (2013) : 2615-2628.
http://dx.doi.org/10.1090/S0002-9939-2013-11532-7
---------- MLA ----------
Pacetti, A. "On the change of root numbers under twisting and applications" . Proceedings of the American Mathematical Society, vol. 141, no. 8, 2013, pp. 2615-2628.
http://dx.doi.org/10.1090/S0002-9939-2013-11532-7
---------- VANCOUVER ----------
Pacetti, A. On the change of root numbers under twisting and applications. Proc. Am. Math. Soc. 2013;141(8):2615-2628.
http://dx.doi.org/10.1090/S0002-9939-2013-11532-7