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Abstract:

Let E be an elliptic curve of rank zero defined over Q{double-struck} and l an odd prime number. For E of prime conductor N, in Quattrini (2006) [Qua06], we remarked that when l||E(Q{double-struck})Tor|, there is a congruence modulo l among a modular form of weight 3/2 corresponding to E and an Eisenstein series. In this work we relate this congruence in weight 3/2, to a well-known one occurring in weight 2, which arises when E(Q{double-struck}) has an l torsion point. For N prime, we prove that this last congruence can be lifted to one involving eigenvectors of Brandt matrices Bp(N) in the quaternion algebra ramified at N and infinity. From this follows the congruence in weight 3/2. For N square free we conjecture on the coefficients of a weight 3/2 Cohen-Eisenstein series of level N, which we expect to be congruent to the weight 3/2 modular form corresponding to E. © 2010 Elsevier Inc.

Registro:

Documento: Artículo
Título:The effect of torsion on the distribution of Sh{cyrillic} among quadratic twists of an elliptic curve
Autor:Quattrini, P.L.
Filiación:Departamento de matemática, FCEyN, Universidad de Buenos Aires, Int. Guiraldes 2160, 1428 Buenos Aires, Argentina
Palabras clave:Congruences of modular forms; Distribution of Sh{cyrillic}; Torsion points of elliptic curves
Año:2011
Volumen:131
Número:2
Página de inicio:195
Página de fin:211
DOI: http://dx.doi.org/10.1016/j.jnt.2010.07.007
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_v131_n2_p195_Quattrini

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Citas:

---------- APA ----------
(2011) . The effect of torsion on the distribution of Sh{cyrillic} among quadratic twists of an elliptic curve. Journal of Number Theory, 131(2), 195-211.
http://dx.doi.org/10.1016/j.jnt.2010.07.007
---------- CHICAGO ----------
Quattrini, P.L. "The effect of torsion on the distribution of Sh{cyrillic} among quadratic twists of an elliptic curve" . Journal of Number Theory 131, no. 2 (2011) : 195-211.
http://dx.doi.org/10.1016/j.jnt.2010.07.007
---------- MLA ----------
Quattrini, P.L. "The effect of torsion on the distribution of Sh{cyrillic} among quadratic twists of an elliptic curve" . Journal of Number Theory, vol. 131, no. 2, 2011, pp. 195-211.
http://dx.doi.org/10.1016/j.jnt.2010.07.007
---------- VANCOUVER ----------
Quattrini, P.L. The effect of torsion on the distribution of Sh{cyrillic} among quadratic twists of an elliptic curve. J. Number Theory. 2011;131(2):195-211.
http://dx.doi.org/10.1016/j.jnt.2010.07.007