Intersections of higher weight cycles and modular forms
Invariants des groupes modulaires de Hilbert sur un corps quadratique
Jacobi forms over imaginary quadratic number fields
Kronecker’s solution of Pell’s equation for CM fields
We generalize Kronecker’s solution of Pell’s equation to CM fields whose Galois group over is an elementary abelian 2-group. This is an identity which relates CM values of a certain Hilbert modular function to products of logarithms of fundamental units. When is imaginary quadratic, these CM values are algebraic numbers related to elliptic units in the Hilbert class field of . Assuming Schanuel’s conjecture, we show that when has degree greater than 2 over these CM values are transcendental....
Mixed Automorphic Forms and Invariants of Elliptic Surfaces.
Mixed Jacobi-like forms of several variables.
Modularity of fibres in rigid local systems.
Modularity of Galois representations
This paper is essentially the text of the author’s lecture at the 2001 Journées Arithmétiques. It addresses the problem of identifying in Galois-theoretic terms those two-dimensional, -adic Galois representations associated to holomorphic Hilbert modular newforms.
Modulflächen quadratischer Dikriminante.
Motives for Hilbert modular forms.
Motives over totally real fields and -adic -functions
Special values of certain functions of the type are studied where is a motive over a totally real field with coefficients in another field , andis an Euler product running through maximal ideals of the maximal order of andbeing a polynomial with coefficients in . Using the Newton and the Hodge polygons of one formulate a conjectural criterium for the existence of a -adic analytic continuation of the special values. This conjecture is verified in a number of cases related to...
Multi-Tensors of Diferential Forms on the Hilbert Modular Variety and on its Subvarieties.
Near holomorphy of some automorphic forms at critical points.
Non annulation des fonctions des formes modulaires de Hilbert au point central
La conjecture de Birch et Swinnerton-Dyer donne des estimations fines sur le rang de certaines variétés abéliennes définies sur . Dans le cas des jacobiennes des courbes modulaires, ce problème est équivalent à l’estimation de l’ordre d’annulation en des fonctions des formes modulaires, et a été traité inconditionnellement par Kowalski, Michel et VanderKam. L’objet de ce travail est d’étendre cette approche dans le cas d’un corps totalement réel arbitraire, ce qui nécessite l’utilisation de...
On a Conjecture of Hecke Concerning Elementary Class Number Formulas.
On Artin L-Functions Associated to Hilbert Modular Forms of Weight One.
On explicit construction of Hilbert-Siegel modular forms of degree two
On Galois representations associated to Hilbert modular forms.
On Galois representations associated to Hilbert modular forms.
On Hilbert modular forms modulo p: explicit ring structure.
H. P. F. Swinnerton-Dyer determined the structure of the ring of modular forms modulo p in the elliptic modular case. In this paper, the structure of the ring of Hilbert modular forms modulo p is studied. In the case where the discriminant of corresponding quadratic field is 8 (or 5), the explicit structure is determined.