ndependence of Modular Units on Tate Curves.
Near holomorphy of some automorphic forms at critical points.
Nearly Holomorphic Functions on Hermitian Symmetric Spaces.
Nearly ordinary deformations of irreducible residual representations
New examples of modular rigid Calabi-Yau threefolds.
The aim of this article is to present five new examples of modular rigid Calabi-Yau threefolds by giving explicit correspondences to newforms of weight 4 and levels 10, 17, 21 and 73.
New forms and Galois representations of octahedral type. (Formes primitives et représentations galoisiennes de type octaédral.)
New identities for the Rogers-Ramanujan functions
New models for the action of Hecke operators in spaces of Maass wave forms
Utilizing the theory of the Poisson transform, we develop some new concrete models for the Hecke theory in a space of Maass forms with eigenvalue on a congruence subgroup . We introduce the field so that consists entirely of algebraic numbers if .The main result of the paper is the following. For a packet of Hecke eigenvalues occurring in we then have that either every is algebraic over , or else will – for some – occur in the first cohomology of a certain space which is a...
New results on Ramanujan's function
Newforms and Functional Equations.
Newforms, inner twists, and the inverse Galois problem for projective linear groups
We reformulate more explicitly the results of Momose, Ribet and Papier concerning the images of the Galois representations attached to newforms without complex multiplication, restricted to the case of weight and trivial nebentypus. We compute two examples of these newforms, with a single inner twist, and we prove that for every inert prime greater than the image is as large as possible. As a consequence, we prove that the groups for every prime , and for every prime , are Galois groups...
Newforms of half-integral weight.
No -torsion on elliptic curves over cubic number fields
We complete our previous determination of the torsion primes of elliptic curves over cubic number fields, by showing that is not one of those.
Nombres de classes et formes modulaires de poids 3/2.
Nombres de Tamagawa des groupes semi-simples
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...
Non standard arithmetic and application to height functions
Non-abelian number fields with very large class numbers
Non-abelian -adic -functions and Eisenstein series of unitary groups – The CM method
In this work we prove various cases of the so-called “torsion congruences” between abelian -adic -functions that are related to automorphic representations of definite unitary groups. These congruences play a central role in the non-commutative Iwasawa theory as it became clear in the works of Kakde, Ritter and Weiss on the non-abelian Main Conjecture for the Tate motive. We tackle these congruences for a general definite unitary group of variables and we obtain more explicit results in the...
Nonanalytic automorphic integrals on the Hecke groups
1. Introduction. Since its genesis over a century ago in work of Jacobi, Riemann, Poincar ́e and Klein [Ja29, Ri53, Le64], the theory of automorphic forms has burgeoned from a branch of analytic number theory into an industry all its own. Natural extensions of the theory are to integrals [Ei57, Kn94a, KS96, Sh94], thereby encompassing Hurwitz’s prototype, the analytic weight 2 Eisenstein series [Hu81], and to nonanalytic forms [He59, Ma64, Sel56, ER74, Fr85]. A generalization in both directions...