M. Eichler, The basis problem for modular forms and the traces of Hecke operators, in Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), pp. 1-36. Lecture Notes in Math., Vol. 320, Springer, Berlin, 1973. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Computing Modular Curves Via Quaternions - Kohel (1998) (Correct)
....and to describe isomorphisms among them. The relation between supersingular elliptic curves and the ideal theory in a quaternion algebra appears in the classical work of Deuring [4] which in the modern theory is properly stated as an equivalence of categories. The basis problem of Eichler [5] provides the means of relating the ideal theory to modular forms. Using this theory Pizer [12] describes an algorithm for computing 1 modular forms. The method of graphs of Oesterl e and Mestre [9] rephrases the theory of quaternion ideals in terms of supersingular elliptic curves. This gives ....
....F ) P q deg = P hA(n)E; F iq n , where the first sum is over all elements of Hom(E;F ) then extending Theta linearly to MQ . That the images lies in M 2 ( Gamma 0 (l) Q) is a well known result for theta functions [14] Eichler proved, as part of his work on the basis problem [5], that MQ and M 2 ( Gamma 0 (l) Q) are isomorphic as Hecke modules. We state this result in the form of the following theorem. Theorem 2 The map T (n) 7 Gamma T 2 (n) of Hecke operators defines an isomorphism of Hecke algebras on MQ and M 2 ( Gamma 0 (l) Q) such that the Brandt morphism ....
M. Eichler. The basis problem for modular forms and the traces of the Hecke operators. In W. Kuyk, editor, Modular Functions of One Variable I, volume 320 of Lecture Notes in Mathematics, pages 75--152. Springer-- Verlag, 1973.
Hecke Module Structure of Quaternions - Kohel (1998) (1 citation) (Correct)
....of the element Eis = X I2S h[I] I]i 1 [I] of M Z Q , de ning the Eisenstein subspace of M . 9 3. 3 Hecke modules of classical modular forms The relation between Hecke modules of quaternions and modular forms is given by the theory of the classical Brandt matrices developed by Eichler [5]. Further aspects of the theory and computation were developed by Pizer [11] The present formulation follows that of Kohel [8] In this theory, there exists a Hecke bilinear pairing with image in the space of modular forms: M M M 2 ( 0 (N) Z) where M is the Hecke module de ned relative ....
M. Eichler. The basis problem for modular forms and the traces of the Hecke operators. In W. Kuyk, editor, Modular Functions of One Variable I, Lecture Notes in Mathematics, 320, Springer-Verlag, 1973, 75-152.
Arithmetic of Modular Curves and Applications - Frey, Müller (1998) (2 citations) (Correct)
....by expanding modular forms into Fourier series. There are other methods to compute the space of modular, respectively cusp forms, for example the algorithm of Birch ( Bir91] which uses ternary quadratic forms. This is a special case of the method of Brandt matrices developed by M. Eichler (see [Eic72]) and generalized by Pizer. Another possibility is Mestre s graph method [Mes86] to compute the space of cusp forms. The modular symbol method works for every level N and the whole space of cusp forms. The other methods are restricted to special levels or they compute only a subspace of the ....
M. Eichler. The Basis Problem for Modular Forms and Traces of the Hecke Operators. In Modular Functions of one Variable I, volume 320 of Lecture Notes in Mathematics, pages 75--152, Berlin, Heidelberg, 1972. Springer-Verlag.
Remarks on Codes From Modular Curves: - Maple Applications David (Correct)
No context found.
M. Eichler, The basis problem for modular forms and the traces of Hecke operators, in Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), pp. 1-36. Lecture Notes in Math., Vol. 320, Springer, Berlin, 1973.
Action of modular correspondences around CM - Jean-Marc Couveignes And (Correct)
No context found.
M. Eichler. The basis problem for modular forms and the traces of the hecke operators. Lecture Notes in Math., 320, 1973.
Arithmetic of Modular Curves and Applications - Gerhard Frey And (1999) (2 citations) (Correct)
No context found.
M. Eichler. The Basis Problem for Modular Forms and Traces of the Hecke Operators. In Modular Functions of one Variable I, volume 320 of Lecture Notes in Mathematics, pages 75--152, Berlin, Heidelberg, 1972. Springer-Verlag.
Iwasawa's Main Conjecture for elliptic curves over.. - Bertolini, Darmon (2001) (2 citations) (Correct)
No context found.
M. Eichler, The basis problem for modular forms and the traces of the Hecke operators. Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), pp. 75{ 151. Lecture Notes in Math., Vol. 320, Springer, Berlin, 1973.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC