相关论文: The trace formula of GL(3)

Trace formula is an important method to study the Langlands program. Arthur obtains the existence of stable trace formula for connected reductive group. In this paper, we will give the explicit coarse trace formula of GL(4). In general…

Langlands has introduced a formula for a specific product of orbital integrals in $\mbox{GL}(2, \mathbb{Q})$. Altu\u{g} employs this formula to manipulate the regular elliptic part of the trace formula, with the aim of eliminating the…

We express the discrete noncuspidal terms in the spectral side of the trace formula for GL(2) in terms of orbital integrals, obtaining a geometric expansion for the cuspidal part of the trace formula. Assuming the Ramanujan conjecture for…

In this paper we study the absolute convergence of the spectral side of the Arthur trace formula. We reduce the problem of the absolute convergence to a problem about local components of automorphic representations. The latter problem can…

In the spirit of Arthur's trace formula, we establish a general trace formula for symmetric spaces associated with the variety of involutions of a finite $D$-module where $D$ is a division algebra central over a number field $F$. Such a…

Let G be the group GL(n) over a number field E and let A be the ring of adeles of E. In this paper we prove that the spectral side of the Arthur trace formula for G is absolutely convergent for all integrable rapidly decreasing functions on…

We study some aspects of the geometric side of the Jacquet-Rallis relative trace formula. Globally, we compute each geometric term of the Jacquet-Rallis relative trace formula on the general linear group for regular supported test…

The continuous spectrum to the spectral side of the Arthur-Selberg trace formula is described in terms of intertwining operators, whose normalising factors involve quotients of $L$-functions. In this paper, we derive two expressions in the…

Following a scheme inspired by B. Feigon, we describe the spectral side of a local relative trace formula for $G:= PGL(2,\rm E)$ relative to the symmetric subgroup $H:=PGL(2,\rm F)$ where $\rm E/\rm F$ is an unramified quadratic extension…

Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function field of a curve defined over a finite field. We also…

Let F be a global function field with constant field $\mathbb{F}_q$. Let G be a reductive group over $\mathbb{F}_q$. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original…

We deduce from Arthur's trace formula a formula with only orbital integrals on the geometric side.

We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of a central simple algebra over a number field $F$ containing a quadratic field extension $E/F$. It is an equality between a sum of geometric distributions on…

We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the following reductive groups over number fields:…

We establish an infinitesimal version of the Jacquet-Rallis trace formula for general linear groups. Our formula is obtained by integrating a kernel truncated a la Arthur multiplied by the absolute value of the determinant to the power $s…

We pursue Arthur's invariant trace formula for certain coverings of connected reductive groups by deducing explicit formulas for its spectral side. This is based on some results in local harmonic analysis from an earlier preprint. The…

We establish the coarse relative trace formulae of Jacquet-Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral…

We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums…

We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of $(GL_{2n,D}, GL_{n,D}\times GL_{n,D})$. It is a kind of Poisson summation formula obtained by an analogue of Arthur's truncation process. It consists in the…

This note provides an informal introduction, with examples, to some technical aspects of the re-normalization of measures on orbital integrals used in the work of Langlands, Frenkel-Langlands-Ng\^o, and Altug on Beyond Endoscopy. In…