Congruences between modular forms and lowering the level mod
In this article we study the behavior of inertia groups for modular Galois mod representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. [9]).
Congruences between Siegel modular forms on the level of group cohomology
Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...
Congruences entre séries d'Eisenstein, dans le cas supersingulier.
Congruences et formes modulaires
Congruences for Eigenvalues of Hecke Operators on Siegel Modular Forms of Degree Two.
Congruences for Eigenvalues of Hecke Operators on SL2(Z).
Congruences for Siegel modular forms
We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree . In particular, we determine when an analog of Atkin’s -operator applied to a Siegel modular form of degree is nonzero modulo a prime . Furthermore, we discuss explicit examples to illustrate our results.
Congruences for the coefficients of quotients of Eisenstein series
Congruences for the Coefficients of the Modular Invariant j(...).
Congruences for the Coefficients of the Modular Invariant j(...).
Congruences for the Fourier coefficients of certain modular forms.
Congruences modulo between factors for cuspidal representations of
Let be two different prime numbers, let be a local non archimedean field of residual characteristic , and let be an algebraic closure of the field of -adic numbers , the ring of integers of , the residual field of . We proved the existence and the unicity of a Langlands local correspondence over for all , compatible with the reduction modulo in [V5], without using and factors of pairs. We conjecture that the Langlands local correspondence over respects congruences modulo between...
Congruences of Cusp Forms and Special Values of Their Zeta Functions.
Conjugacy, Genus, and Class Numbers.
Conjugations of Arithmetic Automorphic Function Fields.
Constructing an automorphic form from the orbit of a transformation.
Constructing elliptic curves over finite fields using double eta-quotients
We examine a class of modular functions for whose values generate ring class fields of imaginary quadratic orders. This fact leads to a new algorithm for constructing elliptic curves with complex multiplication. The difficulties arising when the genus of is not zero are overcome by computing certain modular polynomials.Being a product of four -functions, the proposed modular functions can be viewed as a natural generalisation of the functions examined by Weber and usually employed to construct...
Constructing modular forms from harmonic Maass Jacobi forms
We construct a family of modular forms from harmonic Maass Jacobi forms by considering their Taylor expansion and using the method of holomorphic projection. As an application we present a certain type Hurwitz class relations which can be viewed as a generalization of Mertens' result in M. H. Mertens (2016).
Construction de formes automorphes réflectives sur un espace de dimension 4
Dans la lignée des travaux de V. Gritsenko et V. Nikulin, par des méthodes reliées aux formes de Jacobi définies relativement au réseau de racines on construit six formes automorphes réflectives qui seront associées à des algèbres de Kac–Moody hyperboliques de type de Borcherds, pour la signature et, pour quatre d’entre elles, on précisera une identité du type “formule du dénominateur”, déterminant entièrement l’algèbre en question.
Construction of eigenvarieties in small cohomological dimensions for semi-simple, simply connected groups.