Related papers: Stabilization of the trace formula for metaplectic…

We state a variant of Arthur's weighted fundamental lemma for the metaplectic group of Weil, which will be an essential ingredient of the stable trace formula. Over a local field of large enough residual characteristic, we give a proof…

We establish some results in local harmonic analysis which are necessary for Arthur's invariant trace formula for coverings of connected reductive groups. More precisely, for local coverings we will study (1) the Plancherel formula and its…

We generalize the Shimura-Waldspurger correspondence, which describes the generic part of the automorphic discrete spectrum of the metaplectic group $\mathrm{Mp}_2$, to the metaplectic group $\mathrm{Mp}_{2n}$ of higher rank. To establish…

This paper develops a formalism of endoscopy for the metaplectic group. We define the notions of stable conjugacy, elliptic endoscopic groups, correspondence of semisimple geometric conjugacy classes and the transfer factors in this…

We show that the distributions occurring in the geometric and spectral side of the twisted Arthur-Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven…

We describe an approach to express the geometric side of the Arthur-Selberg trace formula in terms of zeta integrals attached to prehomogeneous vector spaces. This will provide explicit formulas for weighted orbital integrals and for the…

The local trace formula gives strong relations between two types of invariant distributions on a reductive group defined over a local field: orbital integrals and characters of representations. For connected reductive groups, the formula…

We show that continuous bounded group cohomology stabilizes along the sequences of real or complex symplectic Lie groups, and deduce that bounded group cohomology stabilizes along sequences of lattices in them, such as…

We consider the time-harmonic electromagnetic transmission problem for the unit sphere. Appealing to a vector spherical harmonics analysis, we prove the first stability result of the local multiple trace formulation (MTF) for…

A trace formula for Toeplitz operators was proved by Boutet de Monvel and Guillemin in the setting of general Toeplitz structures. Here we give a local version of this result for a class of Toeplitz operators related to continuous groups of…

Let $\widetilde{\mathrm{Sp}}(2n)$ be the metaplectic covering of $\mathrm{Sp}(2n)$ over a local field of characteristic zero. The core of the theory of endoscopy for $\widetilde{\mathrm{Sp}}(2n)$ is the geometric transfer of orbital…

It is the last paper of a long series. We present the spectral side of the twisted trace formula and its stable version. Using the method of Arthur, we finish the proof of the stabilization of the two sides of this twisted trace formula.

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

We consider an oriented version of the stable symplectic category defined in \cite{N}. We show that the group of monoidal automorphisms of this category, that fix each object, contains a natural subgroup isomorphic to the solvable quotient…

It is the second article of a series whose final goal is the stabilization of the twisted trace formula. Over a non archimedean field, we define (after Arthur) wheighted orbital integrals and their stable and endoscopic versions. We state…

We adapt the conjectural local Langlands parameterization to split metaplectic groups over local fields. When $\tilde G$ is a central extension of a split connected reductive group over a local field (arising from the framework of Brylinski…

This thesis provides an explicit, general trace formula for the Hecke and Casimir eigenvalues of GL(2)-automorphic representations over a global field. In special cases, we obtain Selberg's original trace formula. Computations for the…

Given a split classical group of symplectic type and a split general linear group over a local field $F$, we use Langlands-Shahidi method to construct their Rankin-Selberg local $\gamma$-factors and prove the corresponding analytic…

We prove stable versions of trace theorems on the sphere in $L^2$ with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into $L^q$ for $q > 2$, by…

We prove formulas for power moments for point counts of elliptic curves over a finite field $k$ such that the groups of $k$-points of the curves contain a chosen subgroup. These formulas express the moments in terms of traces of Hecke…