Formes modulaires de poids
Formes quadratiques à 4 variables et relèvement
Fourier Coefficients of Cusp Forms.
From pseudodifferential analysis to modular form theory
Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.
Functoriality and the Inverse Galois problem II: groups of type and
This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ? Let be a prime and a positive integer. We show that that the finite simple groups of Lie type if and appear as Galois groups over , for some divisible by . In particular, for each of the two Lie types and fixed we construct infinitely many Galois groups but we do not have a precise control...
Generalized Eisenstein series and modified Dedekind sums.
Geodesic cycles and the Weil representation I ; quotients of hyperbolic space and Siegel modular forms
Heegner cycles, modular forms and jacobi forms
We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.
Hybrid sup-norm bounds for Hecke–Maass cusp forms
Let be a Hecke–Maass cusp form of eigenvalue and square-free level . Normalize the hyperbolic measure such that and the form such that . It is shown that for all . This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.
Hyperbolic distribution problems and half-integral weigth Maass forms.
Hypothèse de Riemann et formes automorphes de Maass
Identités de MacDonald
Improper Eisenstein Series on Bruhat-Tits Trees.
Introduction aux formes modulaires. Formes modulaires -adiques
-functions of automorphic forms and combinatorics: Dyck paths
We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the -functions of modular forms of and . We deduce some results about the asymptotics of these moments. We extend this interpretation to the moments twisted by the eigenvalues of Hecke operators.
Le système d’Euler de Kato
Ce texte est consacré au système d’Euler de Kato, construit à partir des unités modulaires, et à son image par l’application exponentielle duale (loi de réciprocité explicite de Kato). La présentation que nous en donnons est sensiblement différente de la présentation originelle de Kato.
Les nilradicaux différentiels d’anneaux associés aux groupes triangulaires de Riemann-Schwarz
Mémoire de Langlands sur la dimension des espaces de formes automorphes
Metaplectic forms
Mixed automorphic forms and differential equations.