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Abstract:

We describe a general method to compute weight- 3 2 modular forms “associated” with a given weight-2 modular form f of level N, and relate its Fourier coefficients to central values of quadratic twists (real and imaginary) of L(f, s). We will focus on examples for levels N = 27, N = 15, and N = 75. © A K Peters, Ltd.

Registro:

Documento: Artículo
Título:Computing central values of twisted l-series: The case of composite levels
Autor:Pacetti, A.; Tornaría, G.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, Buenos Aires, C.P:1428, Argentina
Facultad de Ciencias, Iguá 4225 esq, Mataojo, Montevideo, Uruguay
Palabras clave:L-series; Quadratic twists; Shimura correspondence
Año:2008
Volumen:17
Número:4
Página de inicio:459
Página de fin:471
DOI: http://dx.doi.org/10.1080/10586458.2008.10128877
Título revista:Experimental Mathematics
Título revista abreviado:Exp. Math.
ISSN:10586458
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10586458_v17_n4_p459_Pacetti

Referencias:

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  • Conrey, J., Keating, J., Rubinstein, M., Snaith, N., On the Frequency of Vanishing of Quadratic Twists of Modular L-Functions (2002) Number Theory for the Millennium I, pp. 301-315. , Wellesley, MA: A K Peters
  • Conrey, J., Keating, J., Rubinstein, M., Snaith, N., Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms (2006) Exp. Math, 15, pp. 67-82
  • Cremona, J., (2008) Elliptic Curve Data, , http://www.maths.nott.ac.uk/personal/jec/ftp/data/INDEX.html
  • Delaunay, C., Note on the Frequency of Vanishing of L-Functions of Elliptic Curves in a Family of Quadratic Twists (2007) Ranks of Elliptic Curves and Random Matrix Theory, pp. 195-200. , London Mathematical Society, Lecture Note Series 341. Cambridge: Cambridge University Press
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  • Kohnen, W., Newforms of Half-Integral Weight (1982) J. Reine Angew. Math, 333, pp. 32-72
  • Mao, Z., Rodriguez-Villegas, F., Tornaría, G., Computation of Central Value of Quadratic Twists of Modular L-Functions (2007) Ranks of Elliptic Curves and Random Matrix Theory, London Mathematical Society, Lecture Note Series 341, pp. 273-288. , Cambridge: Cambridge University Press
  • Pacetti, A., Tornaría, G., Shimura Correspondence for Level p2 and the Central Values of L-Series (2007) J. Number Theory, 124, pp. 396-414
  • Pacetti, A., Tornaría, G., Examples of Shimura Correspondence for Level p2 and Real Quadratic Twists (2007) Ranks of Elliptic Curves and Random Matrix Theory, London Mathematical Society, Lecture Note Series 341, pp. 289-314. , Cambridge: Cambridge University Press
  • Pizer, A., An Algorithm for Computing Modular Forms on Γ (1980) J. Algebra, 64, pp. 340-390
  • 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/cnt
  • Waldspurger, J.-L., Sur les coefficients de Fourier des formes modulaires de poids demi-entier (1981) J. Math. Pures Appl, 60, pp. 375-484

Citas:

---------- APA ----------
Pacetti, A. & Tornaría, G. (2008) . Computing central values of twisted l-series: The case of composite levels. Experimental Mathematics, 17(4), 459-471.
http://dx.doi.org/10.1080/10586458.2008.10128877
---------- CHICAGO ----------
Pacetti, A., Tornaría, G. "Computing central values of twisted l-series: The case of composite levels" . Experimental Mathematics 17, no. 4 (2008) : 459-471.
http://dx.doi.org/10.1080/10586458.2008.10128877
---------- MLA ----------
Pacetti, A., Tornaría, G. "Computing central values of twisted l-series: The case of composite levels" . Experimental Mathematics, vol. 17, no. 4, 2008, pp. 459-471.
http://dx.doi.org/10.1080/10586458.2008.10128877
---------- VANCOUVER ----------
Pacetti, A., Tornaría, G. Computing central values of twisted l-series: The case of composite levels. Exp. Math. 2008;17(4):459-471.
http://dx.doi.org/10.1080/10586458.2008.10128877