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.
Construction of entire modular forms of weights 5 and 6 for the congruence group .
Construction of half integral weight Siegel modular forms of Sp (2, R) from automorphic forms of the compact twist Sp (2).
Construction of Jacobi forms.
Construction of some classes in the cohomology of Siegel modular threefolds
Constructions of automorphic forms and related cohomology classes for arithmetic subgroups of