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Abstract:

Let N ≡ 1 mod 4 be the negative of a prime, K = ℚ(√N) and OK its ring of integers. Let D be a prime ideal in OK of prime norm congruent to 3 mod 4. Under these assumptions, there exists Hecke characters ψD of K with conductor (D) and infinite type (1, 0). Their L-series L (ψD, s) are associated to a CM elliptic curve A(N, D) defined over the Hilbert class field of K. We will prove a Waldspurger-type formula for L(ψD, s) of the form L(ψD, 1) = Ω∑[A],Ir (D, [A], I) m[A],I ([D]) where the sum is over class ideal representatives I of a maximal order in the quaternion algebra ramified at N and infinity and [A] are class group representatives of K. An application of this formula for the case N = -7 will allow us to prove the non-vanishing of a family of L-series of level 7 D over K. © 2005 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:A formula for the central value of certain Hecke L-functions
Autor:Pacetti, A.
Filiación:Departamento de Matemática, Pabellón I, 1428 Buenos Aires, Argentina
Palabras clave:Hecke L-functions
Año:2005
Volumen:113
Número:2
Página de inicio:339
Página de fin:379
DOI: http://dx.doi.org/10.1016/j.jnt.2004.12.004
Título revista:Journal of Number Theory
Título revista abreviado:J. Number Theory
ISSN:0022314X
CODEN:JNUTA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022314X_v113_n2_p339_Pacetti.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022314X_v113_n2_p339_Pacetti

Referencias:

  • Buhler, J., Gross, B., Arithmetic on elliptic curves with complex multiplication II (1985) Invent. Math., 79, pp. 11-29
  • Cassels, J.W.S., (1978) Rational Quadratic Forms, , London: Academic Press Inc
  • Eichler, M., The Basis Problem for Modular Forms and the Traces of the Hecke Operators (1973) Lecture Notes in Mathematics, 320, pp. 75-151. , Springer, Berlin
  • Gross, B., Arithmetic on Elliptic Curves with Complex Multiplication (1980) Lecture Notes in Mathematics, 776. , Springer, Berlin, Heidelberg, New York
  • Gross, B., Heights and the Special Values of L-series (1986) Conference Proceedings of the CMS, 7, pp. 115-187. , American Mathematical Society, Providence, RI
  • Hajir, F., Rodriguez-Villegas, F., Explicit elliptic units (1997) I Duke Math. J., 90 (3)
  • Hecke, E., (1959) Mathematische Werke, , Auftrage der Akademie der Wissenschaften zu Gottingen Vandenhoeck & Ruprecht
  • Mumford, D., Tata lectures on theta I (1983) Progr. Math., 28
  • Ogg, A., (1969) Modular Forms and Dirichlet Series, , New York: W. A. Benjamin
  • Pacetti, A., Rodrigeuz-Villegas, F., Computing weight 2 modular forms of level p2 Math. Comput., , accepted
  • Pizer, A., An algorithm for computing modular forms on Γ0(N) (1980) J. Algebra, 64, pp. 340-390
  • Rodriguez-Villegas, F., On the square root of special values of certain L-series (1991) Invent. Math., 106, pp. 549-573
  • Serre, J.-P., A course in arithmetic (1973) Graduate Texts in Math.
  • Shimura, G., (1998) Abelian Varieties With Complex Multiplication and Modular Functions, Princeton Mathematical Series, 46. , Princeton University Press, Princeton, NJ
  • Shimura, G., On the holomorphy of certain Dirichlet series (1975) Proc. London Math. Soc., 31 (3), pp. 79-98
  • Stark, H., L-functions at s=1. IV. First derivatives at s=0 (1980) Adv. in Math., 35, pp. 197-235
  • Vigneras, M.F., Arithmetique des Algebres de quaternions (1980) Lecture Notes in Mathematics, 800. , Springer, Berlin
  • Waldspurger, J.L., Correspondance de Shimura (1980) J. Math. Pures Appl., 59 (9), pp. 1-132
  • Washington, L., Introduction to cyclotomic fields (1982) Graduate Texts in Math.

Citas:

---------- APA ----------
(2005) . A formula for the central value of certain Hecke L-functions. Journal of Number Theory, 113(2), 339-379.
http://dx.doi.org/10.1016/j.jnt.2004.12.004
---------- CHICAGO ----------
Pacetti, A. "A formula for the central value of certain Hecke L-functions" . Journal of Number Theory 113, no. 2 (2005) : 339-379.
http://dx.doi.org/10.1016/j.jnt.2004.12.004
---------- MLA ----------
Pacetti, A. "A formula for the central value of certain Hecke L-functions" . Journal of Number Theory, vol. 113, no. 2, 2005, pp. 339-379.
http://dx.doi.org/10.1016/j.jnt.2004.12.004
---------- VANCOUVER ----------
Pacetti, A. A formula for the central value of certain Hecke L-functions. J. Number Theory. 2005;113(2):339-379.
http://dx.doi.org/10.1016/j.jnt.2004.12.004